Abstract
Many problems in signal processing and statistical inference involve finding sparse solution to some underdetermined linear system of equations. This is also the application condition of compressive sensing (CS) which can find the sparse solution from the measurements far less than the original signal. In this paper, we proposel1- andl2-norm joint regularization based reconstruction framework to approach the originall0-norm based sparseness-inducing constrained sparse signal reconstruction problem. Firstly, it is shown that, by employing the simple conjugate gradient algorithm, the new formulation provides an effective framework to deduce the solution as the original sparse signal reconstruction problem withl0-norm regularization item. Secondly, the upper reconstruction error limit is presented for the proposed sparse signal reconstruction framework, and it is unveiled that a smaller reconstruction error thanl1-norm relaxation approaches can be realized by using the proposed scheme in most cases. Finally, simulation results are presented to validate the proposed sparse signal reconstruction approach.
Highlights
Compressive sensing or compressive sampling (CS) [1,2,3] is a novel technique that enables efficient sampling below Nyquist rate, without sacrificing reconstruction quality
[21] has shown that lp and l1 − l2 measures are theoretically better than l1-norm to promote sparsity, our analysis shows that the proposed sparse signal reconstruction model can solve the original P0 problem
Simulations are performed to testify the applicability of the proposed signal reconstruction model in different settings
Summary
Compressive sensing or compressive sampling (CS) [1,2,3] is a novel technique that enables efficient sampling below Nyquist rate, without (or with little) sacrificing reconstruction quality. Reference [16] studies a minimization problem where the objective includes a usual l2-norm data-fidelity term and an overlapping group sparsity total variation regularizer, and a fast algorithm is proposed to solve this problem. This method can avoid staircase effect and allow edges preserving. Reference [18] proposes an optimization model for noise and blur removal involving the generalized variation regularization term, the MAP (maximum posterior probability) based data fitting term, and a quadratic penalty term based on the statistical property of the noise This minimization problem can be solved by a primal-dual algorithm.
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