A projected conjugate gradient method for compressive sensing

Authors:
Yuanying Qiu;Wei Xue;Gaohang Yu
Affiliations:
School of Foreign Languages, Gannan Normal University, Ganzhou, People's Republic of China;School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, People's Republic of China;School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, People's Republic of China
Venue:
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Year:
2012

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Abstract

Frequently, the most important information in a signal is much sparser than the signal itself. In this paper, we study a projected conjugate gradient method for finding sparse solutions to an undetermined linear system arising from compressive sensing. The construction of this method consists of two main phases: (1) reformulate a l1 regularized least squares problem into an equivalent nonlinear system of monotone equations; (2) apply a conjugate gradient method with projection strategy to the resulting system. The derived method only needs matrix-vector products at each step and could be easily implemented. Global convergence result is established under some suitable conditions. Numerical results demonstrate that the proposed method can improve the computation time while obtaining similar reconstructed quality.