## Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion |

Optics Express, Vol. 20, Issue 16, pp. 17281-17296 (2012)

http://dx.doi.org/10.1364/OE.20.017281

Acrobat PDF (919 KB)

### Abstract

Compressive fluorescence microscopy has been proposed as a promising approach for fast acquisitions at sub-Nyquist sampling rates. Given that signal-to-noise ratio (SNR) is very important in the design of fluorescence microscopy systems, a new saliency-guided sparse reconstruction ensemble fusion system has been proposed for improving SNR in compressive fluorescence microscopy. This system produces an ensemble of sparse reconstructions using adaptively optimized probability density functions derived based on underlying saliency rather than the common uniform random sampling approach. The ensemble of sparse reconstructions are then fused together via ensemble expectation merging. Experimental results using real fluorescence microscopy data sets show that significantly improved SNR can be achieved when compared to existing compressive fluorescence microscopy approaches, with SNR increases of 16-9 dB within the noise range of 1.5%–10% standard deviation at the same compression rate.

© 2012 OSA

## 1. Introduction

1. H. R. Petty, “Fluorescence microscopy: Established and emerging methods, experimental strategies, and applications in immunology,” Microsc. Res. Tech. **70**(8), 687–709 (2007). [CrossRef] [PubMed]

1. H. R. Petty, “Fluorescence microscopy: Established and emerging methods, experimental strategies, and applications in immunology,” Microsc. Res. Tech. **70**(8), 687–709 (2007). [CrossRef] [PubMed]

1. H. R. Petty, “Fluorescence microscopy: Established and emerging methods, experimental strategies, and applications in immunology,” Microsc. Res. Tech. **70**(8), 687–709 (2007). [CrossRef] [PubMed]

3. S. Inoue and K. R. Spring, *Video Microscopy*New York: Plenum Press13, (1997). [CrossRef]

5. R. Connally, D. Veal, and J. Piper, “High resolution detection of fluorescently labeled microorganisms in environmental samples using time-resolved fluorescence microscopy,” FEMS Microbiol Ecol **41**, 239–245 (2002). [CrossRef] [PubMed]

7. R. Connally, D. Veal, and J. Piper, “Flash lamp-excited time-resolved fluorescence microscope suppresses autofluorescence in water concentrates to deliver an 11-fold increase in signal-to-noise ratio,” J. Biomed. Opt. **9**, 725–734 (2004). [CrossRef] [PubMed]

8. D. Piston, “Choosing objective lenses: The importance of numerical aperture and magnification in digital microscopy,” The Biological Bulletin **195**, 1–4 (1998). [CrossRef] [PubMed]

**70**(8), 687–709 (2007). [CrossRef] [PubMed]

9. R. A. Mathies, K. Peck, and L. Stryer, “Optimization of high-sensitivity fluorescence detection,” Anal. Chem. **62**, 1786–1791 (1990). [CrossRef] [PubMed]

10. L. Song, E. J. Hennink, T. Young, and H. J. Tanke, “Photobleaching kinetics of fluorescein in quantitative fluorescence microscopy,” Biophys. J. **68**, 2588–2600 (1995). [CrossRef] [PubMed]

**70**(8), 687–709 (2007). [CrossRef] [PubMed]

11. N. Panchuk-Voloshina, R. P. Haugland, J. Bishop-Stewart, M. K. Bhalgat, P. J. Millard, F. Mao, W. Leung, and R. P. Haugland, “Alexa dyes, a series of new fluorescent dyes that yield exceptionally bright, photostable conjugates,” J. Histochem. Cytochem. **47**, 1179–1188 (1999). [CrossRef] [PubMed]

12. B. R. Renikuntla, H. C. Rose, J. Eldol, A. S. Waggoner, and B. A. Armitage, “Improved photostability and fluorescence properties through polyfluorination of a cyanine dye,” Organic. Lett. **6**(6), 909–912 (2004). [CrossRef]

^{−6}of the level of excitation light that produced it [2]) and photobleaching effects that limits the excitation light levels provides low SNR. Those limitations can lead to laser confocal microscopy that needs to measure 10–20 photons from brightest pixels in the image and as low as zero or one photon from the background [2]. Beyond physical methods, computational methods have been attempted reduce noise levels through image filters such as anisotropic diffusion and wavelet thresholding [13

13. W. C. Moss, S. Haase, J. M. Lyle, D. A. Agard, and J. W. Sedat, “A novel 3d wavelet-based filter for visualizing features in noisy biological data,” J. Microscopy **219**, 43–49 (2005). [CrossRef]

15. S. Sabri, F. Richelme, A. Pierres, A. Benoliel, and P. Bongrand, “Interest of image processing in cell biology and immunology,” J. Immunol. Methods. **208**, 1–27 (1997). [CrossRef]

16. M. Marim and E. Angelini, “Denoising in fluorescence microscopy using compressed sensing with multiple reconstructions and non-local merging,” Eng. Med. Biol. (EMBC), 2010 Annual International Conference of the IEEE **3394**(7), 3394–3397 (2010). [CrossRef]

19. Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an optical-sectioning compressive sensing microscope (csm),” Opt. Express **18**, 24565–24578 (2010). [CrossRef] [PubMed]

20. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Const. App. **28**(3), 253–263 (2008). [CrossRef]

24. J. Romberg, E. Candes, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory. **52**(2), 489–509 (2006). [CrossRef]

19. Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an optical-sectioning compressive sensing microscope (csm),” Opt. Express **18**, 24565–24578 (2010). [CrossRef] [PubMed]

16. M. Marim and E. Angelini, “Denoising in fluorescence microscopy using compressed sensing with multiple reconstructions and non-local merging,” Eng. Med. Biol. (EMBC), 2010 Annual International Conference of the IEEE **3394**(7), 3394–3397 (2010). [CrossRef]

26. S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” J. Visual Commun. Image Represent. (DOI:http://dx..org/10.1016/j.jvcir.2012.02.002), (2012). [CrossRef]

## 2. Saliency-guided sparse reconstruction ensemble fusion (SSREF) model

20. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Const. App. **28**(3), 253–263 (2008). [CrossRef]

26. S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” J. Visual Commun. Image Represent. (DOI:http://dx..org/10.1016/j.jvcir.2012.02.002), (2012). [CrossRef]

*M*×

*N*sampling locations organized in a finite, separable, rectangular lattice Ω

_{M×N}, with the measured value at each sampling location representing intensity level at that location. Such a lattice can be described as: Let define

*f*as the image representation in spatial domain. Image acquisition is performed in the SSREF model in two phases. In the first phase, which refer as a learning phase,

*f*is sampled sparsely using only 10% of the locations in the scene in order for determinig image regions of interest and creating a subset of salient locations Ω

*. All non-salient locations belongs to subsets Ω*

_{D}*and*

_{S}*is defined based on an operator Γ(*

_{D}*m*,

*n*) that returns a quantitative measure of saliency at sampling location (

*m*,

*n*):

*into three complementary sets Ω*

_{M×N}*, Ω*

_{D}*and*

_{S}*+ Ω*

_{D}*) =*

_{S}*Q*and

*represents locations with high saliency and dense sampling, Ω*

_{D}*represents sparse sampling and*

_{S}*f*is sampled according to saliency-guided method (Eq. (5)).

*K*≤

*NM sampling functions*

*f*can be generally described as where

*k*= 1, 2,...,

*K*and

*e*is added to account for the combined effect of measurement noise and quantization noise.

_{k}*φ*,

_{k}*k*= 1, 2,...,

*K*is sparse, having

*Q*non zero elements, the measurement model (Eq. (4)) needs to be properly adjusted. In particular, we need to account for the fact that there are no observations corresponding to the locations in

*and Ω*

_{D}*are different (Eq. (7), Eq. (8)). Therefore we modify the sampling basis according to Measurements*

_{S}*y*(Eq. (4)) are been formed in two steps: In the first step, which can be referred as the acquisition step, sampling locations (Ω

_{k}*and Ω*

_{D}*) as well as non-sampled locations (*

_{S}19. Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an optical-sectioning compressive sensing microscope (csm),” Opt. Express **18**, 24565–24578 (2010). [CrossRef] [PubMed]

*x*whose probability density is defined in (Eq. (7)) and (Eq. (8)):

*μ*and variance

*p*(Eq. (8)) referred as Gauss-Bernoulli. As such, the proposed sampling function can be practically implemented in a real imaging system via this two-step process.

_{S}*π*≤ 1. Here the pdf of

*α*(

*x*) has zero mean with zero variance, while the probability (1 −

*π*) pdf is normal distributed with zero mean and a variance of

*p*(

_{S}*x*) = 0 with probability

*π*and

*p*(

_{S}*x*) is Gaussian distributed with probability (1 −

*π*). The scene is measured

*T*times by the measurement function (Eq. (6)). Based on this SSREF model, an ensemble of saliency-guided reconstructions

*and Ω*

_{D}*. Finally, the ensemble of reconstructions are then fused to obtain the final reconstructed image*

_{S}*f̃*: where

*E*{.} denotes the fusion function (can be expectation for example) and

*T*is the ensemble size.

## 3. Practical realization of the SSREF model

*S*(

*m*,

*n*) (Eq. (11)), which is high at location (

*m*,

*n*) for situations characterized by large spatial range variations, based on a frequency-tuned saliency map strategy [28

28. R. Achanta, S. Hemami, F. Estrada, and S. Susstrunk, “Frequency-tuned salient region detection,” IEEE International Conference on Computer Vision and Pattern Recognitio pp. 1597–1604 (2009). [CrossRef]

*I*is the mean,

_{μ}*I*(

*m*,

*n*) is the corresponding Laplacian of the Gaussian filtered data, and

*τ*is the threshold value (set at two times the mean saliency

*S*(

*m*,

*n*) of a given data [28

28. R. Achanta, S. Hemami, F. Estrada, and S. Susstrunk, “Frequency-tuned salient region detection,” IEEE International Conference on Computer Vision and Pattern Recognitio pp. 1597–1604 (2009). [CrossRef]

*p*(Eq. (7)) and

_{D}*p*(Eq. (8)) are selected as follows. The probability density function of

_{S}*p*, is a Gaussian distribution with zero mean and unit variance (Eq. (7)) [22

_{D}22. E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. **59**(8), 1207–1221 (2006). [CrossRef]

*p*, is defined as a Gauss-Bernoulli distribution, where

_{S}*p*(

_{S}*x*) = 0 with probability 0.9 and

*p*(

_{S}*x*) is Gaussian distributed with probability 0.1. In order to select the probability

*π*(Eq. (8)), initial experiments were performed. (Fig. 1). This initial experiment for determining high compression rate where CS can still produce reasonably reconstructed data that will be considered for the learning phase. From this initial experiment (Fig. 1) it can be seen, that for very high compression rate (99%) which means that only 1% of the data is used, the learning phase is not sufficient therefore the SSREF reconstruction performance is poor and is even lower then CFM. The reason that SSREF reconstruction performance is lower than CFM is that it is based on insufficient learning data. When 5% of sampling locations are been used, there is a significant improvement to the SSREF reconstruction in comparison to the 1% case. At high compression rates (above 85%) learning using 5% of the samples improves performance compared to learning using 10% of the samples. The reason is that in the 5% case, guided sampling starts at higher compression rate. From the other end, performance of the 10% case is better at lower compression rate because the learning stage relays on more accurate and reliable data therefore is more efficient to identify regions of interest. To achieve a high compression rate in the final phase of SSREF reconstruction while including the sampling locations used for learning to determine compression rate, not considering more than 10% samples for learning is preferable. According to this initial experiment, probability

*π*(Eq. (8)) was selected to be 0.9, representing 90% compression rate or 10% of sampling locations.

*f*is sampled by sparse

*p*(Eq. (13)) using only 10% of the locations in the scene. The saliency function is then used to obtain a rough saliency map of the scene based on the reconstructed fluorescence microscopy image using this first phase. In other words, we determine subset Ω

_{S}*using operator Γ (Eq. (10)).*

_{D}*f*is sampled multiple times by

*p*(Eq. (12)) in order to measure regions of high saliency with higher accuracy. The samples from the two subsets Ω

_{D}*and Ω*

_{D}*are then combined for creating the sampling basis*

_{S}*φ*, with the acquired samples used to reconstruct the fluorescence microscopy image at a higher accuracy than that obtained in the first phase. To reconstruct the image, a ℓ1-based total variation minimization approach was employed. The noise-free range image

_{T,k,t}*f*can be approximated via the following ℓ1-based total variation minimization formulation: where || · ||

_{TVl1}denotes the ℓ1-based anisotropic total variation norm defined by [29

29. A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Imag. Proc. **18**(11), 2419–2434 (2009). [CrossRef]

*λ*> 0 is a regularization constant, and where || · ||

_{2}stands for ℓ2 norm defined by

29. A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Imag. Proc. **18**(11), 2419–2434 (2009). [CrossRef]

30. A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imag. Sci. **1**, 183–202 (2009). [CrossRef]

*n*times (based on empirical testing,

*n*= 10 was found to produce strong results) through

*T*acquisitions at Ω

*and Ω*

_{D}*measurement locations to create an ensemble of*

_{S}*T*saliency-guided reconstructions

*f*̃ is computed via ensemble expectation merging [17] (Eq. (9))

## 4. Experimental results and discussion

### 4.1. Experimental setup

31. M. Riffle and T. N. Davis, “The Yeast Resource Center Public Image Repository: A large database of fluorescence microscopy images,” http://images.yeastrc.org/imagerepo/searchImageRepoInit.do.

*μ*m × 0.12758

*μ*m, objective: 100× and image size 512×512. In addition, three noisy data sets were used for the real noise experiments: YRC PIR ID: 3499, 5352 and 8565. The data sets contain time series of at least 10 images, with the following imaging settings: pixel size: 0.12758

*μ*m × 0.12758

*μ*m, objective: 100× and image size 512×512.

### 4.2. Experiment 1 - noise sensitivity tests

### 4.3. Experiment 2 - compression rate sensitivity tests

*ρ*is defined as one minus the ratio between the number of sampling locations measured and the total number of sampling locations. Therefore, the higher the compression rate achieved, the fewer the number of measurements made. For illustrative purposes, the SNR was measured for fluorescence microscopy image, contaminated with 3% standard deviation noise and reconstructed via ensembles of 10 reconstructions across the range of 0% – 80% compression rates.

### 4.4. Experiment 3 - noisy fluorescence microscopy reconstruction tests

### 4.5. Reconstruction examples

### 4.6. Summary of testing

- The SSREF method produces significantly higher SNR under different synthetic noise scenarios when compared to existing CFM systems (9 to 16 dB within the entire tested noise range).
- The reconstruction performance of the SSREF method increases as the ensemble size increases.
- The SSREF method produces significantly higher SNR under different compression rates (up to 11 dB) when compared to existing CFM systems.
- The SSREF method produces fluorescence microscopy images from real noisy measurements with noticeably better image detail when compared to existing systems.

## 5. Conclusions and future work

**18**, 24565–24578 (2010). [CrossRef] [PubMed]

## Acknowledgment

## References and links

1. | H. R. Petty, “Fluorescence microscopy: Established and emerging methods, experimental strategies, and applications in immunology,” Microsc. Res. Tech. |

2. | J. B. Pawley and B. R. Masters, “Handbook of biological confocal microscopy, third edition,” J. Bio-Med. Opt. |

3. | S. Inoue and K. R. Spring, |

4. | J. Zakrzewski, “Integrating a spectrometer with an optical microscope presents challenges,” SPIE Magazine pp. 29 (2003). |

5. | R. Connally, D. Veal, and J. Piper, “High resolution detection of fluorescently labeled microorganisms in environmental samples using time-resolved fluorescence microscopy,” FEMS Microbiol Ecol |

6. | R. Connally, D. Veal, and J. Piper, “Novel flashlamp based timeresolved fluorescence microscope reduces autofluorescence for 30-fold contrast enhancement in environmental samples,” Proc. SPIE |

7. | R. Connally, D. Veal, and J. Piper, “Flash lamp-excited time-resolved fluorescence microscope suppresses autofluorescence in water concentrates to deliver an 11-fold increase in signal-to-noise ratio,” J. Biomed. Opt. |

8. | D. Piston, “Choosing objective lenses: The importance of numerical aperture and magnification in digital microscopy,” The Biological Bulletin |

9. | R. A. Mathies, K. Peck, and L. Stryer, “Optimization of high-sensitivity fluorescence detection,” Anal. Chem. |

10. | L. Song, E. J. Hennink, T. Young, and H. J. Tanke, “Photobleaching kinetics of fluorescein in quantitative fluorescence microscopy,” Biophys. J. |

11. | N. Panchuk-Voloshina, R. P. Haugland, J. Bishop-Stewart, M. K. Bhalgat, P. J. Millard, F. Mao, W. Leung, and R. P. Haugland, “Alexa dyes, a series of new fluorescent dyes that yield exceptionally bright, photostable conjugates,” J. Histochem. Cytochem. |

12. | B. R. Renikuntla, H. C. Rose, J. Eldol, A. S. Waggoner, and B. A. Armitage, “Improved photostability and fluorescence properties through polyfluorination of a cyanine dye,” Organic. Lett. |

13. | W. C. Moss, S. Haase, J. M. Lyle, D. A. Agard, and J. W. Sedat, “A novel 3d wavelet-based filter for visualizing features in noisy biological data,” J. Microscopy |

14. | P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern. Anal. Mach. Intell. |

15. | S. Sabri, F. Richelme, A. Pierres, A. Benoliel, and P. Bongrand, “Interest of image processing in cell biology and immunology,” J. Immunol. Methods. |

16. | M. Marim and E. Angelini, “Denoising in fluorescence microscopy using compressed sensing with multiple reconstructions and non-local merging,” Eng. Med. Biol. (EMBC), 2010 Annual International Conference of the IEEE |

17. | M. Marim, E. Angelini, and J. C. Olivo-Marin, “Compressed sensing in biological microscopy,” in Proc. SPIE Wavelets XIII |

18. | V. Studer, J. Bobin, M. Chahid, H. Moussavi, E. J. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences of the United States of America pp. 10 (2011). |

19. | Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an optical-sectioning compressive sensing microscope (csm),” Opt. Express |

20. | R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Const. App. |

21. | E. Candes and J. Romberg, “Quantitative robust uncertainty principles and optimally sparse decompositions,” Found. Comput. Math. |

22. | E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. |

23. | D. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory. |

24. | J. Romberg, E. Candes, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory. |

25. | S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive fluorescence microscopy” In 34th Int. Conf. Eng. Med. Biol. (EMBC 2012) (to be published). |

26. | S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” J. Visual Commun. Image Represent. (DOI:http://dx..org/10.1016/j.jvcir.2012.02.002), (2012). [CrossRef] |

27. | E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique |

28. | R. Achanta, S. Hemami, F. Estrada, and S. Susstrunk, “Frequency-tuned salient region detection,” IEEE International Conference on Computer Vision and Pattern Recognitio pp. 1597–1604 (2009). [CrossRef] |

29. | A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Imag. Proc. |

30. | A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imag. Sci. |

31. | M. Riffle and T. N. Davis, “The Yeast Resource Center Public Image Repository: A large database of fluorescence microscopy images,” http://images.yeastrc.org/imagerepo/searchImageRepoInit.do. |

**OCIS Codes**

(100.2000) Image processing : Digital image processing

(180.2520) Microscopy : Fluorescence microscopy

(100.3008) Image processing : Image recognition, algorithms and filters

**ToC Category:**

Microscopy

**History**

Original Manuscript: March 29, 2012

Revised Manuscript: June 19, 2012

Manuscript Accepted: July 3, 2012

Published: July 16, 2012

**Virtual Issues**

Vol. 7, Iss. 9 *Virtual Journal for Biomedical Optics*

**Citation**

Shimon Schwartz, Alexander Wong, and David A. Clausi, "Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion," Opt. Express **20**, 17281-17296 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-16-17281

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### References

- H. R. Petty, “Fluorescence microscopy: Established and emerging methods, experimental strategies, and applications in immunology,” Microsc. Res. Tech.70(8), 687–709 (2007). [CrossRef] [PubMed]
- J. B. Pawley and B. R. Masters, “Handbook of biological confocal microscopy, third edition,” J. Bio-Med. Opt.13(029902), (2008).
- S. Inoue and K. R. Spring, Video MicroscopyNew York: Plenum Press13, (1997). [CrossRef]
- J. Zakrzewski, “Integrating a spectrometer with an optical microscope presents challenges,” SPIE Magazine pp. 29 (2003).
- R. Connally, D. Veal, and J. Piper, “High resolution detection of fluorescently labeled microorganisms in environmental samples using time-resolved fluorescence microscopy,” FEMS Microbiol Ecol41, 239–245 (2002). [CrossRef] [PubMed]
- R. Connally, D. Veal, and J. Piper, “Novel flashlamp based timeresolved fluorescence microscope reduces autofluorescence for 30-fold contrast enhancement in environmental samples,” Proc. SPIE4964, 14–23 (2003). [CrossRef]
- R. Connally, D. Veal, and J. Piper, “Flash lamp-excited time-resolved fluorescence microscope suppresses autofluorescence in water concentrates to deliver an 11-fold increase in signal-to-noise ratio,” J. Biomed. Opt.9, 725–734 (2004). [CrossRef] [PubMed]
- D. Piston, “Choosing objective lenses: The importance of numerical aperture and magnification in digital microscopy,” The Biological Bulletin195, 1–4 (1998). [CrossRef] [PubMed]
- R. A. Mathies, K. Peck, and L. Stryer, “Optimization of high-sensitivity fluorescence detection,” Anal. Chem.62, 1786–1791 (1990). [CrossRef] [PubMed]
- L. Song, E. J. Hennink, T. Young, and H. J. Tanke, “Photobleaching kinetics of fluorescein in quantitative fluorescence microscopy,” Biophys. J.68, 2588–2600 (1995). [CrossRef] [PubMed]
- N. Panchuk-Voloshina, R. P. Haugland, J. Bishop-Stewart, M. K. Bhalgat, P. J. Millard, F. Mao, W. Leung, and R. P. Haugland, “Alexa dyes, a series of new fluorescent dyes that yield exceptionally bright, photostable conjugates,” J. Histochem. Cytochem.47, 1179–1188 (1999). [CrossRef] [PubMed]
- B. R. Renikuntla, H. C. Rose, J. Eldol, A. S. Waggoner, and B. A. Armitage, “Improved photostability and fluorescence properties through polyfluorination of a cyanine dye,” Organic. Lett.6(6), 909–912 (2004). [CrossRef]
- W. C. Moss, S. Haase, J. M. Lyle, D. A. Agard, and J. W. Sedat, “A novel 3d wavelet-based filter for visualizing features in noisy biological data,” J. Microscopy219, 43–49 (2005). [CrossRef]
- P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern. Anal. Mach. Intell.12, 629–639 (1990). [CrossRef]
- S. Sabri, F. Richelme, A. Pierres, A. Benoliel, and P. Bongrand, “Interest of image processing in cell biology and immunology,” J. Immunol. Methods.208, 1–27 (1997). [CrossRef]
- M. Marim and E. Angelini, “Denoising in fluorescence microscopy using compressed sensing with multiple reconstructions and non-local merging,” Eng. Med. Biol. (EMBC), 2010 Annual International Conference of the IEEE3394(7), 3394–3397 (2010). [CrossRef]
- M. Marim, E. Angelini, and J. C. Olivo-Marin, “Compressed sensing in biological microscopy,” in Proc. SPIE Wavelets XIII7446, 3394–3397 (2009).
- V. Studer, J. Bobin, M. Chahid, H. Moussavi, E. J. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences of the United States of America pp. 10 (2011).
- Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an optical-sectioning compressive sensing microscope (csm),” Opt. Express18, 24565–24578 (2010). [CrossRef] [PubMed]
- R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Const. App.28(3), 253–263 (2008). [CrossRef]
- E. Candes and J. Romberg, “Quantitative robust uncertainty principles and optimally sparse decompositions,” Found. Comput. Math.6(2), 227–254 (2006). [CrossRef]
- E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math.59(8), 1207–1221 (2006). [CrossRef]
- D. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory.52(4), 1289–1306 (2006). [CrossRef]
- J. Romberg, E. Candes, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory.52(2), 489–509 (2006). [CrossRef]
- S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive fluorescence microscopy” In 34th Int. Conf. Eng. Med. Biol. (EMBC 2012) (to be published).
- S. Schwartz, A. Wong, and D. A. Clausi, “Saliency-guided compressive sensing approach to efficient laser range measurement,” J. Visual Commun. Image Represent. (DOI: http://dx..org/10.1016/j.jvcir.2012.02.002 ), (2012). [CrossRef]
- E. J. Candes, “Restricted isometry property and its implications for compressed sensing,” Comptes rendus - Mathematique346(9–10), 589–592 (2008).
- R. Achanta, S. Hemami, F. Estrada, and S. Susstrunk, “Frequency-tuned salient region detection,” IEEE International Conference on Computer Vision and Pattern Recognitio pp. 1597–1604 (2009). [CrossRef]
- A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Imag. Proc.18(11), 2419–2434 (2009). [CrossRef]
- A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imag. Sci.1, 183–202 (2009). [CrossRef]
- M. Riffle and T. N. Davis, “The Yeast Resource Center Public Image Repository: A large database of fluorescence microscopy images,” http://images.yeastrc.org/imagerepo/searchImageRepoInit.do .

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