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dc.contributor.authorYang, Junfeng
Zhang, Yin
dc.date.accessioned 2018-06-19T17:45:10Z
dc.date.available 2018-06-19T17:45:10Z
dc.date.issued 2009-11
dc.identifier.citation Yang, Junfeng and Zhang, Yin. "Alternating Direction Algorithms for L1-Problems in Compressive Sensing." (2009) https://hdl.handle.net/1911/102138.
dc.identifier.urihttps://hdl.handle.net/1911/102138
dc.description.abstract In this paper, we propose and study the use of alternating direction algorithms for several L1-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, the basis-pursuit denoising problems of both unconstrained and constrained forms, as well as others. We present and investigate two classes of algorithms derived from either the primal or the dual forms of the L1-problems. The construction of the algorithms consists of two main steps: (1) to reformulate an L1-problem into one having partially separable objective functions by adding new variables and constraints; and (2) to apply an exact or inexact alternating direction method to the resulting problem. The derived alternating direction algorithms can be regarded as first-order primal-dual algorithms because both primal and dual variables are updated at each and every iteration. Convergence properties of these algorithms are established or restated when they already exist. Extensive numerical results in comparison with several state-of-the-art algorithms are given to demonstrate that the proposed algorithms are efficient, stable and robust. Moreover, we present numerical results to emphasize two practically important but perhaps overlooked points. One point is that algorithm speed should always be evaluated relative to appropriate solution accuracy; another is that whenever erroneous measurements possibly exist, the l1-norm fidelity should be the fidelity of choice in compressive sensing.
dc.format.extent 26 pp
dc.title Alternating Direction Algorithms for L1-Problems in Compressive Sensing
dc.type Technical report
dc.date.note November 2009
dc.identifier.digital TR09-37
dc.type.dcmi Text


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