Hard color-shrinkage for color-image processing of a digital color camera

The classic shrinkage works well for monochrome-image denoising. To utilize inter-channel color correlations, a noisy image undergoes the color-transformation from the RGB to the luminance-and-chrominance color space, and the luminance and the chrominance components are separately denoised. However, this approach cannot cope with signaldependent noise of a digital color camera. To utilize the noise's signal-dependencies, previously we have proposed the soft color-shrinkage where the inter-channel color correlations are directly utilized in the RGB color space. The soft color-shrinkage works well; but involves a large amount of computations. To alleviate the drawback, taking up the l0-l2 optimization problem whose solution yields the hard shrinkage, we introduce the l0 norms of color differences and the l0 norms of color sums into the model, and derive hard color-shrinkage as its solution. For each triplet of three primary colors, the hard color-shrinkage has 24 feasible solutions, and from among them selects the optimal feasible solution giving the minimal energy. We propose a method to control its shrinkage parameters spatially-adaptively according to both the local image statistics and the noise's signal-dependencies, and apply the spatially-adaptive hard color-shrinkage to removal of signal-dependent noise in a shift-invariant wavelet transform domain. The hard color-shrinkage performs mostly better than the soft color-shrinkage, from objective and subjective viewpoints.