Signal and Image Restoration

The Problem

During signal and image acquisition, transmission, and storage, signals are corrupted by a variety of processes including noise and blurring.  The Wiener filter is one of the most widely used techniques for image restoration.  This linear shift-invariant filtering method is optimum in a mean squared error (MSE) sense when the signal and noise are jointly Gaussian and stationary.  In many practical applications, however, these conditions are not met.  In such cases, nonlinear and/or spatially adaptive are methods may be needed to obtain desired results.  Dr. Hardie has developed a number of novel nonlinear and spatially adaptive filter classes to address the problem of signal and image restoration in the presence of non-Gaussian and/or non-stationary signals and noise. 

Similar patch selection for the new collaborative adaptive Wiener filter (CAWF).  The CAWF method [1] fuses similar patches to form an estimate of each image pixel in a weighted sum operation.  The weights are based on a new multi-patch correlation model.   Unlike other multi-patch restoration methods, the CAWF method can jointly address noise and blur in a single fusion/restoration step.

Region of interest from the image river with ση=30 Gaussian noise[1]. (a) Truth image, (b) noisy image, (c) AWF, (d) GLIDE-NLM, (e) BM3D, and (f) CAWF.  Mohamed and Hardie EURASIP Journal on Advances in Signal Processing 2015 2015:6   doi:10.1186/s13634-014-0189-3 [2].

Selected References

1. Redha A Almahdi and Russell C Hardie, “Recursive Non-local Means filter for Video Denoising”, EURASIP Journal on Image and Video Processing, 17, April 2017.

2. K. M. Mohamed and R. C. Hardie, “A Collaborative Adaptive Wiener Filter for Image Restoration Using a Spatial-Domain Multi-Patch Correlation Model,” EURASIP Journal on Advances in Signal Processing, 2015, 2015:6  doi:10.1186/s13634-014-0189-3.  (Highly Accessed Status).

3. Y. Lin, R. C. Hardie, Q. Sheng, M. Shao, and K. E. Barner, “Improved Optimization of Soft Partition Weighted Sum Filters and Their Application to Image Restoration,” Appl. Opt. 45, 2697-2706 (2006).

4. Y. Lin, R. C. Hardie, and K. E. Barner, “Subspace partition weighted sum filters for image restoration,” IEEE Signal Processing Letters, Vol. 12 No. 9, September 2005, pp. 613-616.

5. Y. Lin, R. C. Hardie, and K. E. Barner, “Subspace partition weighted sum filters for image deconvolution,” 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2005), Philadelphia, PA, March 2005.

6. E. A. Thompson, R. C. Hardie, and K. E. Barner, “Hybrid Order Statistic Filter and its Application to Image Restoration,” Applied Optics, Vol. 40, No. 5, February 10, 2001, pp. 656-661.

7. K. E. Barner, A. M. Sarhan, and R. C. Hardie, “Partition-Based Weighted Sum Filters for Image Restoration,” IEEE Transactions on Image Processing, Vol. 8, No. 5, May 1999.

8. R. C. Hardie and K. E. Barner, “Extended Permutation Filters and Their Application to Edge Enhancement,” IEEE Transactions on Image Processing, Vol. 5, No. 6, June, 1996, pp. 855-867.

9. R. C. Hardie and K. E. Barner, “Rank Conditioned Rank Selection Filters for Signal Restoration,” IEEE Transactions on Image Processing, Vol. 3, No. 2, March 1994, pp. 192-206.

10. R. C. Hardie and C. G. Boncelet, “LUM Filters: A Class of Rank Order Based Filters for Smoothing and Sharpening,” IEEE Transactions on Signal Processing, Vol. 41, No. 3, March 1993, pp. 1061-1076.

11. R. C. Hardie and G. R. Arce, “Ranking in Rp its use in Multivariate Image Estimation,” IEEE Transactions on Circuits and Systems for Video Technology, Vol. 1, No. 2, June 1991, pp. 197-209