Image denoising using ridgelet transform in a collaborative filtering framework

Redundancy within a natural image has been widely exploited for enhancing the sparsity in representation to achieve better restoration. The BM3D is the current state-of-the-art denoising method. It combines the transform-domain and the non-local means spatial-domain algorithms and is named as “collaborative filtering”. The discrete wavelet transform is shown to be the best performing transform in the collaborative filtering framework for Gaussian noise removal from the natural images. The BM3D is based on the assumption of homogeneity. However, in case of non-homogeneous textured image, there are structures such as lines, curves, etc. which still need to be exploited carefully. Due to the inherent limitations of the wavelets in representing the line singularity, the ridgelet transform was proposed a decade ago. In this paper, we explore the use of ridgelet transform in collaborative filtering framework and show that the BM3D performs better with the ridgelet transform than with the wavelet transform for the denoising textured image.