Sparse Regularization With L~1 Fidelity

This paper mainly focuses on the L1 data fidelity of sparse regularization and its numerical implementation. Besides, the existence of regularized functional solution, stability, convergence and convergence speed are also further discussed. Because the regularization of the data error term and regularization item does not have differentiable nature, it is extremely difficult to figure out its dual form directly. As a result, this paper employs multi-parameter regularization, which adds a L2 smooth off the functional items and a new functional with relatively simple dual structure and smooth characteristic. Finally, projection gradient algorithm is used to find the optimal solution and to prove the algorithm convergence. In the numerical example, according to two different linear inverse problems, the above method is compared with YALL1 algorithms in terms of accuracy and stability. The numerical results verify that the method employed in this paper is a highly efficient and stable method.