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To remove signal-dependent noise of a digital color camera, we propose a new denoising method with our hard color-shrinkage in the tight-frame grouplet transform domain. The classic hard-shrinkage works well for monochrome-image denoising. To utilize inter-channel color dependence, 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; but this approach cannot cope with actual signal-dependent noise. To utilize the noise's signal-dependencies, we have constructed the hard color-shrinkage where the interchannel color dependence is directly utilized in the RGB color space. The hard color-shrinkage alleviates denoising artifacts, and improves picture quality of denoised images.

Alter, Durand and Froment introduced the total-variation (TV) minimization approach to the artifact-free JPEG decoding, which is referred to as the ADF decoding method [1]. They formulated the decoding problem as the constrained TV restoration problem, in which the TV seminorm of its restored color image is minimized under the constraint that each DCT coefficient of the restored color image should be in the quantization interval of its corresponding DCT coefficient of the JPEG-compressed data. This paper proposes a new restoration approach to the JPEG decoding. Instead of the TV regularization, our new JPEG-decoding method employs a shrinkage operation in the redundant DCT domain, to mitigate degradations caused by the JPEG coding. Our new method not only can selectively suppress ringing artifacts near color edges, but also can efficiently eliminate blocking artifacts in originally smoothly-varying image regions, where the blocking artifacts are very noticeable. Through decoding simulations, we experimentally show that our new decoding method can reduce JPEG-coding artifacts more effectively than the ADF decoding method.