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• W72809607 abstract "Tikhonov regularization with p-powers of the weighted lp norms as penalties, with p 2 (1,2), have been employed recently in reconstruction of sparse solutions of ill-posed inverse problems. This paper shows convergence rates for such a regularization with respect to the norm of the weighted spaces by assuming that the solutions satisfy a certain smoothness (source) condition . The meaning of the latter is analyzed in some detail. Moreover, converse results are established: Linear conver gence rates for the residual, together with convergence of the approximations to the solution, can be achieved only if the solution satisfies a source condition. Further insights for the particular case of a convolution equation a re provided by analyzing the equation both theoretically and numerically." @default.
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• W72809607 date "2010-01-01" @default.
• W72809607 modified "2023-10-17" @default.
• W72809607 title "CONVERGENCE RATES FOR REGULARIZATION WITH SPARSITY CONSTRAINTS" @default.
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