Color shrinkage for sparse coding of color images

As a basic tool for deriving sparse representation of a color image from its atomic-decomposition with a redundant dictionary, this paper presents a new kind of shrinkage, viz. color shrinkage, which utilizes inter-channel color cross-correlations directly in the three primary color space. Among various schemes of color shrinkage, this paper particularly addresses the hard color-shrinkage, a natural extension of the classic hard-shrinkage, and shows the advantages over the existing shrinkage approach where the classic hard-shrinkage is applied after a non-redundant color transformation. Moreover, to mitigate defects of the existing shrinkage approach, this paper presents a new simple color-shrinkage scheme that applies the classic hard-shrinkage together with a redundant color transformation instead of a non-redundant color transformation. Furthermore, this paper applies our color-shrinkage schemes to color-image denoising in the tight-frame Haar wavelet transform domain, and experimentally demonstrates their superiority over the existing shrinkage approach.