An Adaptive Iteratively Weighted Half Thresholding Algorithm for Image Compressive Sensing Reconstruction

The \( L_{1/2} \) regularization has been considered as a more effective relaxation method to approximate the optimal \( L_{0} \) sparse solution than \( L_{1} \) in CS. To improve the recovery performance of \( L_{1/2} \) regularization, this study proposes a multiple sub-wavelet-dictionaries-based adaptive iteratively weighted \( L_{1/2} \) regularization algorithm (called MUSAI-\( L_{1/2} \)), and considering the key rule of the weighted parameter (or regularization parameter) in optimization progress, we propose the adaptive scheme for parameter \( \lambda_{d} \) to weight the regularization term which is a composition of the sub-dictionaries. Numerical experiments confirm that the proposed MUSAI-\( L_{1/2} \) can significantly improve the recovery performance than the previous works.