Luminance constrained total variation and its application for optimized decoding of JPEG 2000

We propose a new semi-norm named luminance constrained total variation (LCTV) to utilize a correlation and an imbalance of information amounts between luminance and chrominance for solving image recovery problems. As an example of LCTV application, we also propose a method for restoring chrominance components of JPEG 2000 compressed images. We cast this method into an ℓ₁ (LCTV)-ℓ₂ combined optimization problem. The algorithm to solve this optimization problem by using variable splitting is also proposed and its convergence is confirmed. Experimental results show our proposed optimized decoding method outperforms the existing state-of-the-art denoising methods.