Patch based image denoising using the finite ridgelet transform for less artifacts

• Edge regions are the main source for potential denoising performance improvement.
• Use finite ridgelet transform for better preservation of local geometric structure.
• The optimal aggregation step in patch based overcomplete framework is simplified.
• Best results (PSNR, SSIM and visual quality) in denoising white noise images.
• Denoised natural images demonstrate good visual quality with the least artifacts.

Patch based denoising methods have proved to lead to state-of-the-art results. However, in contrast with intensive pursuing of higher peak signal to noise ratio (PSNR), less attention is paid to visual quality improvement of denoised images. In this paper, we first compare the denoising performance in edge and smooth regions. Results reveal that edge regions are the main source for potential performance improvement. This motivates us to investigate the use of the finite ridgelet transform as a local transform for better preservation of directional singularities. A two stage denoising algorithm is then proposed to improve the representation of detail structures. Experimental results in denoising images which only contain white noise show that the proposed algorithm consistently outperforms other methods in terms of PSNR and Structural SIMilarity index. Denoised images by the proposed method also demonstrate good visual quality with the least artifacts and fake structures in experiments on natural images.