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Compressive sensing (CS) is an effective approach for compressive recovery, such as the imaging problems. It aims at recovering sparse signal or image from a small number of under-sampled data by taking advantage of the sparse signal structure. <inline-formula> <tex-math notation="LaTeX">$L_{1/2}$ </tex-math></inline-formula>-norm regularization in CS framework has been considered as a typical nonconvex relaxation approach to approximate the optimal sparse solution, and can obtain stronger sparse solution than <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula>-norm regularization. However, it is very difficult to solve the nonconvex optimization problem efficiently resulted by <inline-formula> <tex-math notation="LaTeX">$L_{1/2}$ </tex-math></inline-formula>-norm. In order to improve the performance of <inline-formula> <tex-math notation="LaTeX">$L_{1/2}$ </tex-math></inline-formula>-norm regularization and extend the application, we propose a multiple sub-wavelet dictionaries-based adaptively-weighted iterative half thresholding algorithm (MUSAI-<inline-formula> <tex-math notation="LaTeX">$L_{1/2}$ </tex-math></inline-formula>) for sparse signal recovery. In particular, we propose an adaptive-weighting scheme for the regularization parameter to control the tradeoff between the fidelity term and the multiple sub-regularization terms. Numerical experiments are conducted on some typical compressive imaging problems to demonstrate that the proposed MUSAI-<inline-formula> <tex-math notation="LaTeX">$L_{1/2}$ </tex-math></inline-formula> algorithm can yield significantly improved the recovery performance compared with the prior work.

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MUSAI-<inline-formula> <tex-math notation="LaTeX">${L}_{{1/2}}$ </tex-math></inline-formula>: MUltiple Sub-Wavelet-Dictionaries-Based Adaptively-Weighted Iterative Half Thresholding Algorithm for Compressive Imaging

MUSAI- ${L}_{{1/2}}$ : MUltiple Sub-Wavelet-Dictionaries-Based Adaptively-Weighted Iterative Half Thresholding Algorithm for Compressive Imaging