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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 4 — May. 22, 2013
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Blind-deconvolution optical-resolution photoacoustic microscopy in vivo

Jianhua Chen, Riqiang Lin, Huina Wang, Jing Meng, Hairong Zheng, and Liang Song  »View Author Affiliations


Optics Express, Vol. 21, Issue 6, pp. 7316-7327 (2013)
http://dx.doi.org/10.1364/OE.21.007316


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Abstract

Optical-resolution photoacoustic microscopy (OR-PAM) is becoming a vital tool for studying the microcirculation system in vivo. By increasing the numerical aperture of optical focusing, the lateral resolution of OR-PAM can be improved; however, the depth of focus and thus the imaging range will be sacrificed correspondingly. In this work, we report our development of blind-deconvolution optical-resolution photoacoustic microscopy (BD-PAM) that can provide a lateral resolution ~2-fold finer than that of conventional OR-PAM (3.04 vs. 5.78μm), without physically increasing the system’s numerical aperture. The improvement achieved with BD-PAM is demonstrated by imaging graphene nanoparticles and the microvasculature of mice ears in vivo. Our results suggest that BD-PAM may become a valuable tool for many biomedical applications that require both fine spatial resolution and extended depth of focus.

© 2013 OSA

1. Introduction

During the past decade, photoacoustic tomography (PAT) has rapidly emerged as a new biomedical imaging modality [1

1. L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012). [CrossRef] [PubMed]

, 2

2. H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24(7), 848–851 (2006). [CrossRef] [PubMed]

]. In PAT, a short pulsed laser beam is used to illuminate the region of interest of the biological tissue. The tissue’s absorption of this pulsed light energy then induces an instantaneous temperature rise and transient thermoelastic expansion, leading to ultrasonic emissions—also termed as photoacoustic waves—from the tissue. As a result, PAT combines the advantages of rich optical contrast with high ultrasonic resolution at depth, enabling a wide array of biomedical applications, including clinical and preclinical tumor imaging [3

3. S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt. 14(2), 024007 (2009). [CrossRef] [PubMed]

, 4

4. J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt. 17(5), 056016 (2012). [CrossRef] [PubMed]

], functional microvascular angiography [5

5. S. Hu and L. V. Wang, “Photoacoustic imaging and characterization of the microvasculature,” J. Biomed. Opt. 15(1), 011101 (2010). [CrossRef] [PubMed]

7

7. Z. Xie, W. Roberts, P. Carson, X. Liu, C. Tao, and X. Wang, “Evaluation of bladder microvasculature with high-resolution photoacoustic imaging,” Opt. Lett. 36(24), 4815–4817 (2011). [CrossRef] [PubMed]

], atherosclerotic vulnerable plaque identification [8

8. T. J. Allen, A. Hall, A. P. Dhillon, J. S. Owen, and P. C. Beard, “Spectroscopic photoacoustic imaging of lipid-rich plaques in the human aorta in the 740 to 1400 nm wavelength range,” J. Biomed. Opt. 17(6), 061209 (2012). [CrossRef] [PubMed]

10

10. S. Sethuraman, J. H. Amirian, S. H. Litovsky, R. W. Smalling, and S. Y. Emelianov, “Spectroscopic intravascular photoacoustic imaging to differentiate atherosclerotic plaques,” Opt. Express 16(5), 3362–3367 (2008). [CrossRef] [PubMed]

], imaging in ophthalmology [11

11. S. Hu, B. Rao, K. Maslov, and L. V. Wang, “Label-free photoacoustic ophthalmic angiography,” Opt. Lett. 35(1), 1–3 (2010). [CrossRef] [PubMed]

13

13. S. Jiao, M. Jiang, J. Hu, A. Fawzi, Q. Zhou, K. K. Shung, C. A. Puliafito, and H. F. Zhang, “Photoacoustic ophthalmoscopy for in vivo retinal imaging,” Opt. Express 18(4), 3967–3972 (2010). [CrossRef] [PubMed]

], and cerebral imaging [14

14. X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21(7), 803–806 (2003). [CrossRef] [PubMed]

, 15

15. J. Laufer, E. Zhang, G. Raivich, and P. Beard, “Three-dimensional noninvasive imaging of the vasculature in the mouse brain using a high resolution photoacoustic scanner,” Appl. Opt. 48(10), D299–D306 (2009). [CrossRef] [PubMed]

].

Photoacoustic microscopy (PAM) is a major implementation embodiment of PAT [1

1. L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012). [CrossRef] [PubMed]

]. Typically, PAM employs a single broadband focused ultrasonic transducer to detect the optical-absorption-encoded photoacoustic waves. Unlike photoacoustic computed tomography (PACT) that requires software-based image reconstruction [16

16. J. Meng, L. V. Wang, L. Ying, D. Liang, and L. Song, “Compressed-sensing photoacoustic computed tomography in vivo with partially known support,” Opt. Express 20(15), 16510–16523 (2012). [CrossRef]

, 17

17. J. Meng, L. V. Wang, D. Liang, and L. Song, “In vivo optical-resolution photoacoustic computed tomography with compressed sensing,” Opt. Lett. 37(22), 4573–4575 (2012). [CrossRef] [PubMed]

], PAM directly acquires photoacoustic A-lines—reflecting the tissue’s local optical absorption properties as a function of depth—using the signals’ time-of-arrival information. With raster scanning, volumetric PAM images can be obtained, without the need of a reconstruction algorithm.

Optical-resolution photoacoustic microscopy (OR-PAM) is one form of PAM developed for micrometer- or sub-micrometer-scale high-resolution imaging [18

18. K. Maslov, H. F. Zhang, S. Hu, and L. V. Wang, “Optical-resolution photoacoustic microscopy for in vivo imaging of single capillaries,” Opt. Lett. 33(9), 929–931 (2008). [CrossRef] [PubMed]

20

20. R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, and D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express 3(7), 1724–1731 (2012). [CrossRef] [PubMed]

], which is critical for important biomedical applications such as the study of tumor angiogenesis [21

21. S. Oladipupo, S. Hu, J. Kovalski, J. Yao, A. Santeford, R. E. Sohn, R. Shohet, K. Maslov, L. V. Wang, and J. M. Arbeit, “VEGF is essential for hypoxia-inducible factor-mediated neovascularization but dispensable for endothelial sprouting,” Proc. Natl. Acad. Sci. U.S.A. 108(32), 13264–13269 (2011). [CrossRef] [PubMed]

]. In addition to the use of a focused ultrasonic transducer for detection, OR-PAM employs a focused laser beam for photoacoustic excitation. Generally, to optimize the detection efficiency, the light illumination and the sound detection are set confocally and coaxially. In the lateral (or transverse) direction of OR-PAM, the dimension of the focused laser spot is much smaller than that of the focused acoustic detection. As a result, the lateral resolution in OR-PAM is almost solely determined by the focusing of the excitation light. In the axial (or depth) direction, OR-PAM directly achieves sectioning by resolving the time-of-arrival differences of the photoacoustic signals. Hence, the axial resolution is decoupled from the lateral one, and primarily determined by the ultrasonic transducer’s bandwidth profile.

Since the lateral resolution of OR-PAM is defined by optical focusing, a straightforward method for improving it is to increase the optical numerical aperture (NA). Recently, a microscope objective with a NA of 0.63 has been adopted in reflection-mode OR-PAM to achieve sub-micrometer resolution [22

22. C. Zhang, K. Maslov, S. Hu, R. Chen, Q. Zhou, K. K. Shung, and L. V. Wang, “Reflection-mode submicron-resolution in vivo photoacoustic microscopy,” J. Biomed. Opt. 17(2), 020501 (2012). [CrossRef] [PubMed]

]. However, high-NA optical focusing also introduces shortcomings: first, a high-NA system is sensitive to even tiny optical imperfections, and thus additional correcting optics is usually needed to compensate the induced aberrations [18

18. K. Maslov, H. F. Zhang, S. Hu, and L. V. Wang, “Optical-resolution photoacoustic microscopy for in vivo imaging of single capillaries,” Opt. Lett. 33(9), 929–931 (2008). [CrossRef] [PubMed]

, 20

20. R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, and D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express 3(7), 1724–1731 (2012). [CrossRef] [PubMed]

]; second, the depth of focus (DOF) is inversely proportional to the square of NA, meaning that the in-focus depth shrinks sharply with an increased NA; third, the working distance (WD) of the objective also decreases with an increased NA, reducing the flexibility of the system for in vivo imaging. Therefore, alternative approaches capable of improving the spatial resolution without physically increasing the NA of the system are quite valuable.

Sophisticated signal processing methods have long been developed for conventional optical microscopy to achieve optical sectioning, leading to the emergence of deconvolution microscopy [23

23. D. A. Agard and J. W. Sedat, “Three-dimensional architecture of a polytene nucleus,” Nature 302(5910), 676–681 (1983). [CrossRef] [PubMed]

, 24

24. J.-B. Sibarita, “Deconvolution Microscopy,” Adv. Biochem. Eng. Biotechnol. 95, 201–243 (2005). [CrossRef] [PubMed]

]. In order to improve the contrast and spatial resolution, deconvolution has now been widely adopted in other optical imaging technologies, such as confocal microscopy [25

25. M. Laasmaa, M. Vendelin, and P. Peterson, “Application of regularized Richardson-Lucy algorithm for deconvolution of confocal microscopy images,” J. Microsc. 243(2), 124–140 (2011). [CrossRef] [PubMed]

], two-photon microscopy [26

26. X. Lv, “Modified robust anisotropic diffusion denoising technique with regularized Richardson-Lucy deconvolution for two-photon microscopic images,” Opt. Eng. 47(4), 047004 (2008). [CrossRef]

, 27

27. C. F. Gainer, U. Utzinger, and M. Romanowski, “Scanning two-photon microscopy with upconverting lanthanide nanoparticles via Richardson-Lucy deconvolution,” J. Biomed. Opt. 17(7), 076003 (2012). [CrossRef] [PubMed]

], and optical coherence tomography (OCT) [28

28. G. Liu, S. Yousefi, Z. Zhi, and R. K. Wang, “Automatic estimation of point-spread-function for deconvoluting out-of-focus optical coherence tomographic images using information entropy-based approach,” Opt. Express 19(19), 18135–18148 (2011). [CrossRef] [PubMed]

, 29

29. T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE. Trans. Img. Proc 14(9), 1254–1264 (2005). [CrossRef]

]. Recently, deconvolution methods have also been developed to improve the image quality of PACT [30

30. C. Zhang, C. Li, and L. V. Wang, “Fast and robust deconvolution-based image reconstruction for photoacoustic tomography in circular geometry: experimental validation,” IEEE. Photonics. J. 2(1), 57–66 (2010). [CrossRef]

32

32. T. Jetzfellner and V. Ntziachristos, “Performance of Blind Deconvolution in Optoacoustic Tomography,” JIOHS 04(04), 385–393 (2011).

]. However, so far, although the development of new OR-PAM technologies has been rapid [33

33. L. Zeng, G. Liu, D. Yang, and X. Ji, “Portable optical-resolution photoacoustic microscopy with a pulsed laser diode excitation,” Appl. Phys. Lett. 102(5), 053704 (2013). [CrossRef]

, 34

34. L. Zeng, G. Liu, D. Yang, and X. Ji, “3D-visual laser-diode-based photoacoustic imaging,” Opt. Express 20(2), 1237–1246 (2012). [CrossRef] [PubMed]

], the exploration of deconvolution in OR-PAM has been limited to only the simplest model and Wiener Filtering [35

35. C. Zhang, K. Maslov, J. Yao, and L. V. Wang, “In vivo photoacoustic microscopy with 7.6-µm axial resolution using a commercial 125-MHz ultrasonic transducer,” J. Biomed. Opt. 17(11), 116016 (2012). [CrossRef] [PubMed]

], which require a prior knowledge of the point spread function (PSF) of the system. In practice, it can be quite challenging to accurately measure the PSF of an OR-PAM system in vivo. Hence, the use of Wiener Filtering for deconvolution in OR-PAM provides only very limited improvement for in vivo imaging.

In this work, for the first time to our knowledge, we have explored the use of blind deconvolution in OR-PAM, which requires no prior knowledge of the PSF of the system. Compared with conventional OR-PAM, the approach developed in this work—blind deconvolution optical-resolution photoacoustic microscopy, or BD-PAM—is capable of providing significantly improved lateral resolution and image contrast. Specifically, imaging of graphene nanoparticles has demonstrated that BD-PAM can provide a lateral resolution approximately two times finer than that of conventional OR-PAM (3.04μm vs. 5.78μm, with an effective NA of ~0.05), breaking through the optical diffraction limit without modification of the system’s hardware. Since this lateral-resolution improvement is obtained without physically increasing the NA of the optical focusing of the system, a relatively large DOF (~0.43mm) is maintained. Further imaging of the microvasculature in mice ears in vivo has demonstrated the superiority of BD-PAM over conventional OR-PAM (of the same NA) in revealing fine biological structures such as the capillary beds and networks.

2. Methods

2.1 OR-PAM system

Figure 1
Fig. 1 Schematic of the OR-PAM system. AP, aperture; CL, convex lens; FC, fiber coupler; SMF, single mode fiber; Obj, objective; RM, reflection mirror; UST, ultrasonic transducer; AL, acoustic lens; SO, silicone oil; EA, electrical amplifier; DAQ, data acquisition; PC, personal computer.
illustrates the schematic of the OR-PAM system. An Nd:YAG pulsed laser (SPOT-532, Elforlight) was operated at a 532-nm wavelength with a repetition rate of 2kHz. The emitted laser beam with a pulse duration of around 1.8ns was reshaped by a circular aperture of 2mm in diameter. Then, the beam was coupled into a 3.5μm-core single mode fiber via an assembled fiber coupler (F-91, Newport). The output beam from the fiber was collimated using a microscope objective (PLN4X, Olympus, NA: 0.1) for further focusing. Reflected by a mirror, the collimated beam was then focused by another identical objective to provide micrometer-scale focused optical illumination into the tissue below the water dish. For in vivo imaging, the laser energy reaching the biological tissue was ~100nJ per pulse, corresponding to an optical fluence of ~19mJ/cm2 on the skin surface (when focused ~200μm below the skin surface), which conforms to the 20mJ/cm2 ANSI safety standards (the maximum permissible exposure). Medical-grade ultrasound gel was evenly dispensed between the animal and water tank for acoustic coupling. Photoacoustic waves emitted from the tissue propagated through the water and the rhomboidal prism, getting totally reflected at the silicone oil layer filled between the rhomboidal and triangular prisms, and then being detected by a 75-MHz ultrasonic transducer (V2022, Olympus-NDT) placed on the top surface of the rhomboidal prism. The detected signals were pre-amplified using a commercial electrical amplifier (ZFL-500LN-BNC + , Mini-Circuits), digitized via a 200-MS/s data acquisition (DAQ) card (CS1422, GaGe), and then stored in a personal computer. A 6-mm-in-diameter acoustic lens (45006, Edmund, acoustic NA: 0.43) was firmly attached to the bottom of the rhomboidal prism to enhance receiving sensitivity by confocally aligning the optical and acoustic foci. Volumetric OR-PAM images were obtained with mechanical raster scanning via precisely programmed electrical scanners (PLS-85, Micos). The imaging speed of the OR-PAM system, limited by the speed of mechanical scanning, was ~0.5 frame (B-scan) per second.

Theoretically, the optical diffraction-limited lateral resolution defined in full width at half maximum (FWHM) of the PSF can be calculated by
Resolution=0.51λNA,
(1)
where λ denotes the laser wavelength and NA denotes the numerical aperture of the optical illumination. In our case, the acoustic lens and prisms reduced the effective NA of the system from 0.1 (objective NA) to ~0.05, which was confirmed with both a Zemax simulation and experimental measurements (see below). Hence, the lateral resolution in expectation was calculated to be ~5.43μm at a laser wavelength of 532nm.

In order to experimentally measure the lateral resolution of our OR-PAM, the edge of a sharp metallic blade was imaged (with unidirectional B-scanning only). Figure 2
Fig. 2 Measurement of the line spread function (LSF) using the edge of a sharp metallic blade. Blue scattered asterisk: original photoacoustic signal; green dash line: edge spread function (ESF); red solid line: the first-order derivative of the ESF, representing the LSF along the scanning direction.
plots the photoacoustic signal amplitude (blue asterisk) as a function of the lateral distance across the edge. The line spread function (LSF) in the scanning direction was derived from the first-order derivative of the edge spread function (ESF) and the FWHM resolution was estimated to be 5.70μm, slightly large but very close to the theoretical value of 5.43μm.

2.2 Richardson-Lucy blind deconvolution

In most cases, an imaging system can be assumed linear and spatially shift invariant. Taking the presence of additive noise into account, the relationship between the original true object o(x,y) and the output image g(x,y) of the system can be represented as
g(x,y)=h(x,y)o(x,y)+n(x,y),
(2)
where * denotes the convolution operator in a 2-D plane, h(x,y) denotes the PSF of the system, and n(x,y) denotes the random spatial distribution of noise. The goal of blind deconvolution is to seek the optimal estimation of h(x,y) and o(x,y) (i.e., h'(x,y) and o'(x,y)) from g(x,y).

The Richardson-Lucy (RL) algorithm was initially developed from Bayes’ theorem with a known system PSF. Derived from the maximum-likelihood estimation approach, the iterative representation to finding o'(x,y) is given by [36

36. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62(1), 55–59 (1972). [CrossRef]

, 37

37. L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79(6), 745–754 (1974). [CrossRef]

]
oi+1'(x,y)=[g(x,y)h(x,y)oi'(x,y)*h(x,y)]oi'(x,y),
(3)
where i is the number of iteration and h(x,y) is the PSF of the system. Usually, the initial guess of the object o'0(x,y) is set as g(x,y) to start the iteration. Then, one can find o'(x,y) by simply iterating Eq. (3) until its convergence.

In the blind deconvolution form of this algorithm (h(x,y) is unknown), two similar RL deconvolution iterations are performed. At the kth iteration, the estimated PSF h'k(x,y) from one iterative branch was substituted into the other one to find the estimated object o'k(x,y), which can be written as [38

38. D. A. Fish, A. M. Brinicombe, E. R. Pike, and J. G. Walker, “Blind deconvolution by means of the Richardson-Lucy algorithm,” J. Opt. Soc. Am. A 12(1), 58–65 (1995). [CrossRef]

]
hk'(x,y)=[g(x,y)hk1'(x,y)ok1'(x,y)*ok1'(x,y)]hk1'(x,y)ok'(x,y)=[g(x,y)ok1'(x,y)hk'(x,y)*hk'(x,y)]ok1'(x,y),
(4)
where the initial guess of PSF h'0(x,y) usually comes from a theoretical estimation.

To terminate the iteration loop and quantify the quality of the restored/deconvolved image, two criteria were used in our algorithm: (a) the normalized adjacent mean square error (AMSE) of two estimated images restored in adjacent iterations, as defined by
AMSE=xy[ok'(x,y)ok1'(x,y)]2xyok1'(x,y)2;
(5)
(b) the absolute error ratio (AER), as defined by
AER=xy[ok'(x,y)*hk'(x,y)g(x,y)]2xyg(x,y)2.
(6)
While AMSE was used to evaluate the evolution of fluctuation in successively restored images, AER was used to evaluate the consistency between the restored image and the experimentally acquired one.

3. Results

3.1 Imaging of graphene nanoparticles

We first tested and evaluated the effectiveness of Richardson-Lucy blind deconvolution (RL-BD) by imaging individual graphene nanoparticles of a diameter of ~200nm, which are good approximations of point sources for our OR-PAM. The sample was prepared by dripping a drop of sufficiently diluted grapheme-nanoparticle solution on a glass slide. The distribution of the nanoparticles was made sparse enough, so that some individual particles in an OR-PAM image could be identified.

Figure 3(a)
Fig. 3 Imaging of a single graphene nanoparticle for lateral-resolution quantification. (a) OR-PAM image; (b) BD-PAM image; (c) Photoacoustic amplitude profiles and their corresponding Gaussian fits (Blue: OR-PAM; Red: BD-PAM) along the yellow dash lines; (d) Deconvolved nanoparticle FWHMs and recovered PSFs under different initial PSF guesses.
is the maximum amplitude projection (MAP) along the depth direction of a representative volumetric sub-image of a single graphene nanoparticle. The corresponding blind-deconvolution optical-resolution photoacoustic microscopy (BD-PAM) image upon applying RL-BD is shown in Fig. 3(b). In our computation, we used a normalized 2-D Gaussian function with a FWHM of 6μm as the initial guess of PSF, which was slightly larger than but close to the theoretical estimation of the system’s PSF. This pick-up of the initial PSF was consistent with that in reference [39

39. V. Loyev and Y. Yitzhaky, “Initialization of iterative parametric algorithms for blind deconvolution of motion-blurred images,” Appl. Opt. 45(11), 2444–2452 (2006). [CrossRef] [PubMed]

]. To terminate the computation, 10 iterations were performed—when the AMSE reached its first local minimum (~0.001). As shown in Fig. 3(c), the resolution of the original OR-PAM system was measured to be 5.78μm, consistent with the LSF (FWHM: 5.70μm) measurement using the blade edge. In BD-PAM, the lateral resolution (cross-sectional FWHM of the deconvolved nanoparticle image) was improved to 3.04μm, ~2 times finer than that of the original OR-PAM. In addition, using a Gaussian-shaped PSF with different FWHMs as the initial guesses, we evaluated the flexibility and consistency of BD-PAM. Figure 3(d) shows the change of the estimated (recovered) PSFs and the deconvolved nanoparticle FWHMs under different initial guesses. The results suggest that a broad range of initial PSF guesses can be used in our BD-PAM, eliminating the need of knowing the exact PSF of the system.

3.2 In vivo imaging of mice ears

To validate the performance of BD-PAM in vivo, the ear of an anesthetized nude mouse (female BALB/c, around six-week old and weighted ~20g)—Mouse 1—was imaged. All experimental animal procedures were carried out in compliance with protocols approved by the Animal Studies Committee of the Shenzhen Institutes of Advanced Technology, the Chinese Academy of Sciences. Figure 4(a)
Fig. 4 OR-PAM and BD-PAM of a mouse (Mouse 1) ear in vivo. (a) Original OR-PAM image of the microvasculature in the ear; (b) Enlarged OR-PAM sub-image corresponding to the blue dash box in (a); (c) Deconvolved BD-PAM image corresponding to (b).
is an MAP image—formed by projecting the maximum photoacoustic amplitude of each A-line in a volumetric image towards the skin surface—of an area of 10mm × 6mm in the ear. The system’s high resolution has enabled clear identification of capillary-level microvessels. Figure 4(b) shows a 3.2mm × 3.2mm OR-PAM sub-image corresponding to the blue dash box in Fig. 4(a). Figure 4(c) is the deconvolved BD-PAM image corresponding to Fig. 4(b). To improve the deconvolution precision, we did not directly apply RL-BD—a 2D operation—to Fig. 4(b), which is the MAP of a volumetric image. Instead, we first divided the original volumetric image (not shown) corresponding to Fig. 4(b) into 10 section images (each of ~8-μm thick) along the depth direction (within the DOF), and then executed RL-BD on each section (discussed in detail below). A Gaussian function with a FWHM of 15μm was used as the universal initial PSF guess for deconvolving all sections. The number of iterations for termination, however, ranged from eight to ten for different sections. Figure 4(c) is formed by taking the MAP (unless otherwise mentioned, all MAPs are projected along the depth direction in this work) of the volumetric image consisting of the 10 respectively deconvolved section images. Clear improvement of spatial resolution can be seen in Fig. 4(c) when compared with Fig. 4(b).

In Figs. 5(a)
Fig. 5 Representative OR-PAM and BD-PAM axial section images of Mouse 1. (a) Area A in Fig. 4(b). Upper row: original OR-PAM images; lower row: BD-PAM images. (b) Area B in Fig. 4(b). Upper row: original OR-PAM images; lower row: BD-PAM images. (c) AMSE (left axis, solid line) and AER (right axis, dash line) of area A as a function of the number of iterations; (d) AMSE and AER of area B as a function of the number of iterations.
and 5(b), areas A and B corresponding to the white solid boxes in Fig. 4(b) are zoomed in for further comparison, where the original OR-PAM images are listed in the upper row while the deconvolved BD-PAM images are listed in the lower row. The MAP images are placed at the leftmost, followed by three representative section images (each of ~8μm thick) labeled with their sequence numbers representing different depths. It can be seen that, with improved resolution, the details of the capillary networks (beds) are better revealed with BD-PAM than with OR-PAM. The AMSEs and AERs of the section images from both areas A and B were calculated and plotted as a function of the number of iterations, in Figs. 5(c) and (d), respectively. For each section, the optimal result was achieved upon the AMSE reaching its first local minimum. If excessive iterations were performed after that, undesired artifacts would be introduced in the deconvolved images, consistent with the results in reference [40

40. D. S. C. Biggs and M. Andrews, “Acceleration of iterative image restoration algorithms,” Appl. Opt. 36(8), 1766–1775 (1997). [CrossRef] [PubMed]

]. Therefore, with a further increased number of iterations, although the AMSE may reach a second minimum (Figs. 5(c) and 5(d)), the corresponding AER also increases significantly, indicating that the deconvolution has become inaccurate under such conditions.

In addition, to evaluate the flexibility and consistency of BD-PAM in vivo, a series of PSFs with different FWHMs were tested as the initial guesses to deconvolve the 30th section image corresponding to area B in Fig. 4(b). Figure 6(a)
Fig. 6 BD-PAM in vivo (Mouse 1) with initial PSF guesses of different FWHMs. (a) Original OR-PAM image of the 30th axial section corresponding to area B in Fig. 4(b); (b) – (d) Corresponding BD-PAM images with the initially guessed PSF of a FWHM of 10μm, 15μm, and 20μm, respectively.
shows the original OR-PAM image of this section. Figures 6(b)6(d) show the deconvolved images using an initial PSF of a FWHM of 10μm, 15μm, and 20μm, respectively. Each deconvolution process (with a different initial PSF) was terminated upon the corresponding AMSE reaching the first local minimum. It can be seen that a broad range of initial PSF guesses (10 – 20μm in this case) can be used for BD-PAM, eliminating the need of knowing the exact in vivo PSF of the system.

To further validate the reliability of BD-PAM in vivo, the ear of another nude mouse (Mouse 2) was imaged. Again, the improvement in spatial resolution achieved with BD-PAM—over conventional OR-PAM—for identifying fine microvascular features was clearly demonstrated (Figs. 7(a)
Fig. 7 Comparison of in vivo OR-PAM and BD-PAM images of Mouse 2. (a) The original OR-PAM image; (b) BD-PAM image; (c) OR-PAM (upper) and BD-PAM (lower) images of a pair of closely localized microvessels as labeled by arrow A in (a); (d) Cross-sectional profiles corresponding to the white dash lines in (c).
and 7(b)). To better illustrate this improvement, a pair of closely localized microvessels is zoomed in for comparison (Fig. 7(c)). Plotting of the cross-sectional profiles (Fig. 7(d)) unambiguously confirms that BD-PAM has significantly improved the spatial resolution compared with conventional OR-PAM. In addition, by computing the contrast to noise ratio (CNR) of the original OR-PAM and BD-PAM images, respectively, we have found that the CNR was improved by ~2.3 times with BD-PAM.

4. Conclusions

In conclusion, using Richardson-Lucy blind deconvolution, we have developed BD-PAM on top of an OR-PAM system. As demonstrated by imaging individual graphene nanoparticles, BD-PAM provides ~2-fold finer lateral resolution compared with that of the original OR-PAM, without the need of knowing the accurate PSF of the system. Further, in vivo imaging of the microvasculature in mice ears have shown that BD-PAM can consistently provide significantly improved lateral resolution and contrast, with robust performance under a relatively broad range of initial PSF guesses. Most importantly, the improvement in lateral resolution and contrast achieved with BD-PAM does not require a physical increase of the NA of the system; thus a relatively large DOF is maintained. The promising results demonstrated in this work suggest that BD-PAM may become a valuable imaging tool to many biomedical applications that require both fine spatial resolution and an extended imaging range.

Acknowledgment

This work was supported in part by the National Natural Science Foundation of China grant No. 61205203, the Shenzhen Development and Reform Commission grant: [2012] No. 1065 and [2010] No. 1599, the Guangdong Innovation Research Team Fund for Low-cost Healthcare Technologies (GIRTF-LCHT), the Low-cost Health Engineering Research Program of the Chinese Academy of Sciences [2011], and the Start-up Fund of SIAT [2011]. The authors would like to thank Dr. Changhui Li’s group at Peking University for providing us the graphene nanoparticles for resolution measurements, and Dr. Wei Zheng and Ruimin Liu at SIAT for beneficial discussions.

References and links

1.

L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012). [CrossRef] [PubMed]

2.

H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24(7), 848–851 (2006). [CrossRef] [PubMed]

3.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt. 14(2), 024007 (2009). [CrossRef] [PubMed]

4.

J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt. 17(5), 056016 (2012). [CrossRef] [PubMed]

5.

S. Hu and L. V. Wang, “Photoacoustic imaging and characterization of the microvasculature,” J. Biomed. Opt. 15(1), 011101 (2010). [CrossRef] [PubMed]

6.

J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt. 16(7), 076003 (2011). [CrossRef] [PubMed]

7.

Z. Xie, W. Roberts, P. Carson, X. Liu, C. Tao, and X. Wang, “Evaluation of bladder microvasculature with high-resolution photoacoustic imaging,” Opt. Lett. 36(24), 4815–4817 (2011). [CrossRef] [PubMed]

8.

T. J. Allen, A. Hall, A. P. Dhillon, J. S. Owen, and P. C. Beard, “Spectroscopic photoacoustic imaging of lipid-rich plaques in the human aorta in the 740 to 1400 nm wavelength range,” J. Biomed. Opt. 17(6), 061209 (2012). [CrossRef] [PubMed]

9.

K. Jansen, A. F. van der Steen, H. M. van Beusekom, J. W. Oosterhuis, and G. van Soest, “Intravascular photoacoustic imaging of human coronary atherosclerosis,” Opt. Lett. 36(5), 597–599 (2011). [CrossRef] [PubMed]

10.

S. Sethuraman, J. H. Amirian, S. H. Litovsky, R. W. Smalling, and S. Y. Emelianov, “Spectroscopic intravascular photoacoustic imaging to differentiate atherosclerotic plaques,” Opt. Express 16(5), 3362–3367 (2008). [CrossRef] [PubMed]

11.

S. Hu, B. Rao, K. Maslov, and L. V. Wang, “Label-free photoacoustic ophthalmic angiography,” Opt. Lett. 35(1), 1–3 (2010). [CrossRef] [PubMed]

12.

A. de la Zerda, Y. M. Paulus, R. Teed, S. Bodapati, Y. Dollberg, B. T. Khuri-Yakub, M. S. Blumenkranz, D. M. Moshfeghi, and S. S. Gambhir, “Photoacoustic ocular imaging,” Opt. Lett. 35(3), 270–272 (2010). [CrossRef] [PubMed]

13.

S. Jiao, M. Jiang, J. Hu, A. Fawzi, Q. Zhou, K. K. Shung, C. A. Puliafito, and H. F. Zhang, “Photoacoustic ophthalmoscopy for in vivo retinal imaging,” Opt. Express 18(4), 3967–3972 (2010). [CrossRef] [PubMed]

14.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21(7), 803–806 (2003). [CrossRef] [PubMed]

15.

J. Laufer, E. Zhang, G. Raivich, and P. Beard, “Three-dimensional noninvasive imaging of the vasculature in the mouse brain using a high resolution photoacoustic scanner,” Appl. Opt. 48(10), D299–D306 (2009). [CrossRef] [PubMed]

16.

J. Meng, L. V. Wang, L. Ying, D. Liang, and L. Song, “Compressed-sensing photoacoustic computed tomography in vivo with partially known support,” Opt. Express 20(15), 16510–16523 (2012). [CrossRef]

17.

J. Meng, L. V. Wang, D. Liang, and L. Song, “In vivo optical-resolution photoacoustic computed tomography with compressed sensing,” Opt. Lett. 37(22), 4573–4575 (2012). [CrossRef] [PubMed]

18.

K. Maslov, H. F. Zhang, S. Hu, and L. V. Wang, “Optical-resolution photoacoustic microscopy for in vivo imaging of single capillaries,” Opt. Lett. 33(9), 929–931 (2008). [CrossRef] [PubMed]

19.

L. Song, K. Maslov, and L. V. Wang, “Multifocal optical-resolution photoacoustic microscopy in vivo,” Opt. Lett. 36(7), 1236–1238 (2011). [CrossRef] [PubMed]

20.

R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, and D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express 3(7), 1724–1731 (2012). [CrossRef] [PubMed]

21.

S. Oladipupo, S. Hu, J. Kovalski, J. Yao, A. Santeford, R. E. Sohn, R. Shohet, K. Maslov, L. V. Wang, and J. M. Arbeit, “VEGF is essential for hypoxia-inducible factor-mediated neovascularization but dispensable for endothelial sprouting,” Proc. Natl. Acad. Sci. U.S.A. 108(32), 13264–13269 (2011). [CrossRef] [PubMed]

22.

C. Zhang, K. Maslov, S. Hu, R. Chen, Q. Zhou, K. K. Shung, and L. V. Wang, “Reflection-mode submicron-resolution in vivo photoacoustic microscopy,” J. Biomed. Opt. 17(2), 020501 (2012). [CrossRef] [PubMed]

23.

D. A. Agard and J. W. Sedat, “Three-dimensional architecture of a polytene nucleus,” Nature 302(5910), 676–681 (1983). [CrossRef] [PubMed]

24.

J.-B. Sibarita, “Deconvolution Microscopy,” Adv. Biochem. Eng. Biotechnol. 95, 201–243 (2005). [CrossRef] [PubMed]

25.

M. Laasmaa, M. Vendelin, and P. Peterson, “Application of regularized Richardson-Lucy algorithm for deconvolution of confocal microscopy images,” J. Microsc. 243(2), 124–140 (2011). [CrossRef] [PubMed]

26.

X. Lv, “Modified robust anisotropic diffusion denoising technique with regularized Richardson-Lucy deconvolution for two-photon microscopic images,” Opt. Eng. 47(4), 047004 (2008). [CrossRef]

27.

C. F. Gainer, U. Utzinger, and M. Romanowski, “Scanning two-photon microscopy with upconverting lanthanide nanoparticles via Richardson-Lucy deconvolution,” J. Biomed. Opt. 17(7), 076003 (2012). [CrossRef] [PubMed]

28.

G. Liu, S. Yousefi, Z. Zhi, and R. K. Wang, “Automatic estimation of point-spread-function for deconvoluting out-of-focus optical coherence tomographic images using information entropy-based approach,” Opt. Express 19(19), 18135–18148 (2011). [CrossRef] [PubMed]

29.

T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE. Trans. Img. Proc 14(9), 1254–1264 (2005). [CrossRef]

30.

C. Zhang, C. Li, and L. V. Wang, “Fast and robust deconvolution-based image reconstruction for photoacoustic tomography in circular geometry: experimental validation,” IEEE. Photonics. J. 2(1), 57–66 (2010). [CrossRef]

31.

Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004). [CrossRef] [PubMed]

32.

T. Jetzfellner and V. Ntziachristos, “Performance of Blind Deconvolution in Optoacoustic Tomography,” JIOHS 04(04), 385–393 (2011).

33.

L. Zeng, G. Liu, D. Yang, and X. Ji, “Portable optical-resolution photoacoustic microscopy with a pulsed laser diode excitation,” Appl. Phys. Lett. 102(5), 053704 (2013). [CrossRef]

34.

L. Zeng, G. Liu, D. Yang, and X. Ji, “3D-visual laser-diode-based photoacoustic imaging,” Opt. Express 20(2), 1237–1246 (2012). [CrossRef] [PubMed]

35.

C. Zhang, K. Maslov, J. Yao, and L. V. Wang, “In vivo photoacoustic microscopy with 7.6-µm axial resolution using a commercial 125-MHz ultrasonic transducer,” J. Biomed. Opt. 17(11), 116016 (2012). [CrossRef] [PubMed]

36.

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62(1), 55–59 (1972). [CrossRef]

37.

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79(6), 745–754 (1974). [CrossRef]

38.

D. A. Fish, A. M. Brinicombe, E. R. Pike, and J. G. Walker, “Blind deconvolution by means of the Richardson-Lucy algorithm,” J. Opt. Soc. Am. A 12(1), 58–65 (1995). [CrossRef]

39.

V. Loyev and Y. Yitzhaky, “Initialization of iterative parametric algorithms for blind deconvolution of motion-blurred images,” Appl. Opt. 45(11), 2444–2452 (2006). [CrossRef] [PubMed]

40.

D. S. C. Biggs and M. Andrews, “Acceleration of iterative image restoration algorithms,” Appl. Opt. 36(8), 1766–1775 (1997). [CrossRef] [PubMed]

OCIS Codes
(170.0180) Medical optics and biotechnology : Microscopy
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.5120) Medical optics and biotechnology : Photoacoustic imaging

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: January 18, 2013
Revised Manuscript: February 19, 2013
Manuscript Accepted: February 20, 2013
Published: March 15, 2013

Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Jianhua Chen, Riqiang Lin, Huina Wang, Jing Meng, Hairong Zheng, and Liang Song, "Blind-deconvolution optical-resolution photoacoustic microscopy in vivo," Opt. Express 21, 7316-7327 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-6-7316


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References

  1. L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science335(6075), 1458–1462 (2012). [CrossRef] [PubMed]
  2. H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol.24(7), 848–851 (2006). [CrossRef] [PubMed]
  3. S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009). [CrossRef] [PubMed]
  4. J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt.17(5), 056016 (2012). [CrossRef] [PubMed]
  5. S. Hu and L. V. Wang, “Photoacoustic imaging and characterization of the microvasculature,” J. Biomed. Opt.15(1), 011101 (2010). [CrossRef] [PubMed]
  6. J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011). [CrossRef] [PubMed]
  7. Z. Xie, W. Roberts, P. Carson, X. Liu, C. Tao, and X. Wang, “Evaluation of bladder microvasculature with high-resolution photoacoustic imaging,” Opt. Lett.36(24), 4815–4817 (2011). [CrossRef] [PubMed]
  8. T. J. Allen, A. Hall, A. P. Dhillon, J. S. Owen, and P. C. Beard, “Spectroscopic photoacoustic imaging of lipid-rich plaques in the human aorta in the 740 to 1400 nm wavelength range,” J. Biomed. Opt.17(6), 061209 (2012). [CrossRef] [PubMed]
  9. K. Jansen, A. F. van der Steen, H. M. van Beusekom, J. W. Oosterhuis, and G. van Soest, “Intravascular photoacoustic imaging of human coronary atherosclerosis,” Opt. Lett.36(5), 597–599 (2011). [CrossRef] [PubMed]
  10. S. Sethuraman, J. H. Amirian, S. H. Litovsky, R. W. Smalling, and S. Y. Emelianov, “Spectroscopic intravascular photoacoustic imaging to differentiate atherosclerotic plaques,” Opt. Express16(5), 3362–3367 (2008). [CrossRef] [PubMed]
  11. S. Hu, B. Rao, K. Maslov, and L. V. Wang, “Label-free photoacoustic ophthalmic angiography,” Opt. Lett.35(1), 1–3 (2010). [CrossRef] [PubMed]
  12. A. de la Zerda, Y. M. Paulus, R. Teed, S. Bodapati, Y. Dollberg, B. T. Khuri-Yakub, M. S. Blumenkranz, D. M. Moshfeghi, and S. S. Gambhir, “Photoacoustic ocular imaging,” Opt. Lett.35(3), 270–272 (2010). [CrossRef] [PubMed]
  13. S. Jiao, M. Jiang, J. Hu, A. Fawzi, Q. Zhou, K. K. Shung, C. A. Puliafito, and H. F. Zhang, “Photoacoustic ophthalmoscopy for in vivo retinal imaging,” Opt. Express18(4), 3967–3972 (2010). [CrossRef] [PubMed]
  14. X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003). [CrossRef] [PubMed]
  15. J. Laufer, E. Zhang, G. Raivich, and P. Beard, “Three-dimensional noninvasive imaging of the vasculature in the mouse brain using a high resolution photoacoustic scanner,” Appl. Opt.48(10), D299–D306 (2009). [CrossRef] [PubMed]
  16. J. Meng, L. V. Wang, L. Ying, D. Liang, and L. Song, “Compressed-sensing photoacoustic computed tomography in vivo with partially known support,” Opt. Express20(15), 16510–16523 (2012). [CrossRef]
  17. J. Meng, L. V. Wang, D. Liang, and L. Song, “In vivo optical-resolution photoacoustic computed tomography with compressed sensing,” Opt. Lett.37(22), 4573–4575 (2012). [CrossRef] [PubMed]
  18. K. Maslov, H. F. Zhang, S. Hu, and L. V. Wang, “Optical-resolution photoacoustic microscopy for in vivo imaging of single capillaries,” Opt. Lett.33(9), 929–931 (2008). [CrossRef] [PubMed]
  19. L. Song, K. Maslov, and L. V. Wang, “Multifocal optical-resolution photoacoustic microscopy in vivo,” Opt. Lett.36(7), 1236–1238 (2011). [CrossRef] [PubMed]
  20. R. Ma, S. Söntges, S. Shoham, V. Ntziachristos, and D. Razansky, “Fast scanning coaxial optoacoustic microscopy,” Biomed. Opt. Express3(7), 1724–1731 (2012). [CrossRef] [PubMed]
  21. S. Oladipupo, S. Hu, J. Kovalski, J. Yao, A. Santeford, R. E. Sohn, R. Shohet, K. Maslov, L. V. Wang, and J. M. Arbeit, “VEGF is essential for hypoxia-inducible factor-mediated neovascularization but dispensable for endothelial sprouting,” Proc. Natl. Acad. Sci. U.S.A.108(32), 13264–13269 (2011). [CrossRef] [PubMed]
  22. C. Zhang, K. Maslov, S. Hu, R. Chen, Q. Zhou, K. K. Shung, and L. V. Wang, “Reflection-mode submicron-resolution in vivo photoacoustic microscopy,” J. Biomed. Opt.17(2), 020501 (2012). [CrossRef] [PubMed]
  23. D. A. Agard and J. W. Sedat, “Three-dimensional architecture of a polytene nucleus,” Nature302(5910), 676–681 (1983). [CrossRef] [PubMed]
  24. J.-B. Sibarita, “Deconvolution Microscopy,” Adv. Biochem. Eng. Biotechnol.95, 201–243 (2005). [CrossRef] [PubMed]
  25. M. Laasmaa, M. Vendelin, and P. Peterson, “Application of regularized Richardson-Lucy algorithm for deconvolution of confocal microscopy images,” J. Microsc.243(2), 124–140 (2011). [CrossRef] [PubMed]
  26. X. Lv, “Modified robust anisotropic diffusion denoising technique with regularized Richardson-Lucy deconvolution for two-photon microscopic images,” Opt. Eng.47(4), 047004 (2008). [CrossRef]
  27. C. F. Gainer, U. Utzinger, and M. Romanowski, “Scanning two-photon microscopy with upconverting lanthanide nanoparticles via Richardson-Lucy deconvolution,” J. Biomed. Opt.17(7), 076003 (2012). [CrossRef] [PubMed]
  28. G. Liu, S. Yousefi, Z. Zhi, and R. K. Wang, “Automatic estimation of point-spread-function for deconvoluting out-of-focus optical coherence tomographic images using information entropy-based approach,” Opt. Express19(19), 18135–18148 (2011). [CrossRef] [PubMed]
  29. T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE. Trans. Img. Proc14(9), 1254–1264 (2005). [CrossRef]
  30. C. Zhang, C. Li, and L. V. Wang, “Fast and robust deconvolution-based image reconstruction for photoacoustic tomography in circular geometry: experimental validation,” IEEE. Photonics. J.2(1), 57–66 (2010). [CrossRef]
  31. Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol.49(14), 3117–3124 (2004). [CrossRef] [PubMed]
  32. T. Jetzfellner and V. Ntziachristos, “Performance of Blind Deconvolution in Optoacoustic Tomography,” JIOHS04(04), 385–393 (2011).
  33. L. Zeng, G. Liu, D. Yang, and X. Ji, “Portable optical-resolution photoacoustic microscopy with a pulsed laser diode excitation,” Appl. Phys. Lett.102(5), 053704 (2013). [CrossRef]
  34. L. Zeng, G. Liu, D. Yang, and X. Ji, “3D-visual laser-diode-based photoacoustic imaging,” Opt. Express20(2), 1237–1246 (2012). [CrossRef] [PubMed]
  35. C. Zhang, K. Maslov, J. Yao, and L. V. Wang, “In vivo photoacoustic microscopy with 7.6-µm axial resolution using a commercial 125-MHz ultrasonic transducer,” J. Biomed. Opt.17(11), 116016 (2012). [CrossRef] [PubMed]
  36. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am.62(1), 55–59 (1972). [CrossRef]
  37. L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J.79(6), 745–754 (1974). [CrossRef]
  38. D. A. Fish, A. M. Brinicombe, E. R. Pike, and J. G. Walker, “Blind deconvolution by means of the Richardson-Lucy algorithm,” J. Opt. Soc. Am. A12(1), 58–65 (1995). [CrossRef]
  39. V. Loyev and Y. Yitzhaky, “Initialization of iterative parametric algorithms for blind deconvolution of motion-blurred images,” Appl. Opt.45(11), 2444–2452 (2006). [CrossRef] [PubMed]
  40. D. S. C. Biggs and M. Andrews, “Acceleration of iterative image restoration algorithms,” Appl. Opt.36(8), 1766–1775 (1997). [CrossRef] [PubMed]

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