## Image denoising using the ridgelet bi-frame

JOSA A, Vol. 23, Issue 10, pp. 2449-2461 (2006)

http://dx.doi.org/10.1364/JOSAA.23.002449

Acrobat PDF (867 KB)

### Abstract

We are concerned with the performance evaluation of the ridgelet bi-frame for image denoising application. The ridgelet bi-frame is a new (as far as we know) bi-frame system that can efficiently deal with straight singularities in two dimensions. We show that, for images dominated by straight edges, the ridgelet bi-frame can obtain much better restoration results than wavelet systems. We also investigate the statistical properties of the ridgelet bi-frame coefficients of these images. Results indicate that the marginal distribution of ridgelet bi-frame coefficients has higher kurtosis than that of wavelet coefficients of the same images. We describe a simple method through which statistical denoising algorithms previously developed in the wavelet domain can be conveniently introduced into the ridgelet bi-frame domain. In addition, we use the ridgelet bi-frame to construct another new bi-frame system referred to as the curvelet bi-frame, which can be viewed as a generalized version of the curvelet. Experiment results show that the simple hard-threshold procedure in the curvelet bi-frame domain produces restoration results comparable with those due to the state-of-the-art denoising methods.

© 2006 Optical Society of America

**OCIS Codes**

(100.0100) Image processing : Image processing

(100.7410) Image processing : Wavelets

**ToC Category:**

Image Processing

**History**

Original Manuscript: August 9, 2005

Revised Manuscript: January 17, 2006

Manuscript Accepted: April 4, 2006

**Citation**

Shan Tan and Licheng Jiao, "Image denoising using the ridgelet bi-frame," J. Opt. Soc. Am. A **23**, 2449-2461 (2006)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-10-2449

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