2016
DOI: 10.3934/ipi.2016017
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An efficient projection method for nonlinear inverse problems with sparsity constraints

Abstract: In this paper, we propose a modification of the accelerated projective steepest descent method for solving nonlinear inverse problems with an 1 constraint on the variable, which was recently proposed by Teschke and Borries (2010 Inverse Problems 26 025007). In their method, there are some parameters need to be estimated, which is a difficult task for many applications. We overcome this difficulty by introducing a self-adaptive strategy in choosing the parameters. Theoretically, the convergence of their algorit… Show more

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Cited by 3 publications
(8 citation statements)
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“…In this work, the slow convergence of the NLW scheme is alleviated using a self-adaptive version of the PASD algorithm [37], [38]. The original PASD scheme achieves acceleration by confining the solution search within a particular L 1 -norm ball, while maintaining a large iteration step size without sacrificing from accuracy and convergence [37].…”
Section: Self-adaptive Projected Accelerated Steepest Descent Schemementioning
confidence: 99%
See 4 more Smart Citations
“…In this work, the slow convergence of the NLW scheme is alleviated using a self-adaptive version of the PASD algorithm [37], [38]. The original PASD scheme achieves acceleration by confining the solution search within a particular L 1 -norm ball, while maintaining a large iteration step size without sacrificing from accuracy and convergence [37].…”
Section: Self-adaptive Projected Accelerated Steepest Descent Schemementioning
confidence: 99%
“…The original PASD scheme achieves acceleration by confining the solution search within a particular L 1 -norm ball, while maintaining a large iteration step size without sacrificing from accuracy and convergence [37]. Its self-adaptive version, which is proposed in [38] and abbreviated as A-PASD in this paper, further increases the convergence by controlling the step size in a recursive/adaptive manner. This approach starts with a larger step size and decreases it only when necessary.…”
Section: Self-adaptive Projected Accelerated Steepest Descent Schemementioning
confidence: 99%
See 3 more Smart Citations