Wavelet Transforms, Contourlet Transforms and Block Matching Transforms for Denoising of Corrupted Images via Bi-shrink Filter

Objectives: Image Denoising refers to the recovery of an image that has been corrupted by noise due to poor quality of image acquisition and transmission. Accordingly, there is a need to reduce the noise present in the image as a consequence of the denoised image formed. Methods/Statistical Analysis: This paper presents Image denoising using Wavelet transforms, Contourlet transforms and Block Matching Transforms governed by bivariate shrinkage (Bi-shrink) filter techniques. The Wavelet transform uses up-sampling, down-sampling, low pass filter and high pass filter to perform denoising operation, the Contourlet transform uses up-sampling, down-sampling, low pass filter and high pass filter and directional filter banks to perform denoising operation, the Block Matching Transform uses Haar Transforms, Discrete cosine transforms and Karhunen Loeve transform to perform denoising operation. Findings: The performance of wavelet transforms, Contourlet transforms and Block Matching Transforms are evaluated for Reference images (such as towers, shades and ruler images) corrupted by gaussian noise and salt and pepper noise, by computing two error metrics Peak Signal to Noise Ratio (PSNR) and Execution Time (ET) with help of shrinkage function. Programming these using MATLAB R2014a by exploring its wavelet transform, Contourlet transform, image processing and signal processing toolboxes and the values are presented in tabular forms and discussed in the section 6. In this paper the block matching haar discrete cosine transform is proposed for denoising of images (especially for those images possessing detailed textures) that works through haar transform and discrete cosine transform outstrips the basic transform discrete wavelet transform and semi translation invariant contourlet transform. For the images corrupted by Gaussian noise and denoised by the proposed transform outstrips the basic transform “Discrete Wavelet Transform by PSNR = 6.71 dB, ET = 25.89 sec” and “Semi Translation Invariant Contourlet Transforms by PSNR = 5.49 dB, ET = 5.89 sec”. For the images corrupted by Salt and Pepper noise and denoised by the proposed transform outstrips the basic transform “Discrete Wavelet Transform by PSNR = 21.15 dB, ET = 0.27 sec” and “Semi Translation Invariant Contourlet Transforms by PSNR = 20.05 dB, ET = 5.80 sec”. Application/Improvements: In this paper Block Matching Haar Discrete cosine transform is proposed to overcome the limitations of wavelet transforms and Contourlet transforms, hence to attain the trade-off between high peak signal to noise ratio and less execution time. Results and Discussion section illustrates the efficacy of the proposed transform in terms of peak signal to noise ratio, execution time and visual quality of images.