Optimum Co-Design for Image Denoising between Type-2 Fuzzy Identifier and Matrix Completion Denoiser

With the wide deployment of digital image capturing equipment, the need of denoising to produce a crystal clear image from noisy capture environment has become indispensable. In this work, a novel type-2 fuzzy-based filter is proposed for denoising images corrupted by impulse noise, especially for the high-density salt-and-pepper noise. It operates two stages, namely, type-2 fuzzy identifier and matrix completion denoiser. In the proposed method, the type-2 fuzzy identifier is first employed to identify and trim the entries contaminated by impulse noise in the data matrix from fuzzy system. Then, the trimmed data matrix is utilized to retrieve the noiseless data matrix with the matrix completion technology. Herein, a novel matrix completion technique is developed without $a priori$ rank information compared with its counterparts. Simulation results are presented which vividly show the denoised images obtained by the proposed method can achieve crystal clear image with strong structural integrity, and are showing good performance in terms of peak signal-to-noise ratio (PSNR).