Local sparse representation for astronomical image denoising

Motivated by local coordinate coding (LCC) theory in nonlinear manifold learning, a new image representation model called local sparse representation (LSR) for astronomical image denoising was proposed. Borrowing ideas from surrogate function and applying the iterative shrinkage-thresholding algorithm (ISTA), an iterative shrinkage operator for LSR was derived. Meanwhile, a fast approximated LSR method by first performing a K-nearest-neighbor search and then solving a l1 optimization problem was presented under the guarantee of denoising performance. In addition, the LSR model and adaptive dictionary learning were incorporated into a unified optimization framework, which explicitly established the inner connection of them. Such processing allows us to simultaneously update sparse coding vectors and the dictionary by alternating-optimization method. The experimental results show that the proposed method is superior to the traditional denoising method and reaches state-of-the-art performance on astronomical image.