Image Denoising Using Projection on Convex Sets

Krishna Ratakonda

This work addresses the problem of denoising of images corrupted by AWGN. The Wiener filter is optimum in minimizing the mean-square-error under suitable assumptions of stationarity of the signal statistics. Locally, such assumptions are reasonable, as in the adaptive realization of theWiener filter whose performance is among the best known till date. Over the last few years, there has been much interest in threshold based denoising schemes. In this paper we present a novel framework for denoising signals from their compact representation in multiple domains. Each domain captures, uniquely, certain signal characteristics better than others. We define confidence sets around data in each domain and find sparse estimates that lie in the intersection of these sets, using a POCS algorithm. Simulations demonstrate the superior nature of the reconstruction (both in terms of mean-square error and perceptual quality) in comparison to the adaptive Wiener filter.

Results

The following images compare the performance of our scheme to that of Donoho and Johnstone's.

                          

(a)                                                              (b)

 

                          

(c)                                                              (d)

(a) Lena processed with the Donoho-Johnstone scheme (best singleDaubechies filter). PSNR: 33.25 dB. (b) Lena processed with 1-3-4 wavelet filters. PSNR: 35.01 dB. Original noisy image (not shown) PSNR: 31.21 dB. (c) Goldhill processed with the Donoho-Johnstone scheme (best single Daubechies filter). PSNR: 30.59 dB. (d) Goldhill processed with 1-3-5 wavelet filters. PSNR: 33.51 dB. Original noisy image (not shown) PSNR: 29.04 dB.

PSNR as a function of the number of vanishing moments of the wavelet used.

Papers

• Segmentation based denoising using multiple compaction domains
  Singh, M.; Ishwar, P.; Ratakonda, K.; Ahuja, N. Image Processing, 1999. ICIP 99. Proceedings. 1999 International Conference on , Volume: 1 , 1999 Page(s): 372 -375 vol.1
  
• Image denoising using multiple compaction domains
  Ishwar, P.; Ratakonda, K.; Moulin, P.; Ahuja, N. Acoustics, Speech and Signal Processing, 1998. Proceedings of the 1998 IEEE International Conference on , Volume: 3 , 1998 Page(s): 1889 -1892 vol.3
  
  

Contact Information:

Narendra Ahuja
2041 Beckman Institute
405 N. Mathews Avenue, Urbana IL 61801, USA.
Ph: (217) 244-4392 / 333-1869
Fax: (217) 244-8371
Email: nahuja@vision.ai.uiuc.edu

| Home | Projects | People | Publications | Links |