Training dictionary by granular computing with L∞

Considering the objects by different granularity reflects the recognition common law of people, granular computing embodies the transformation between different granularity spaces. We present the image denoising algorithm by using the dictionary trained by granular computing with L∞-norm, which realizes three transformations, (1) the transformation from image space to patch granule space, (2) the transformation between granule spaces with different granularities, and (3) the transformation from patch granule space to image space. We demonstrate that the granular computing with L∞-norm achieved the comparable peak signal to noise ratio (PSNR) measure compared with BM3D and patch group prior based denoising for eight natural images