Abstract
Image reconstruction based on sparse constraints is an important research topic in compressed sensing. Sparsity adaptive matching pursuit (SAMP) is a greedy pursuit reconstruction algorithm, which reconstructs signals without prior information of the sparsity level and potentially presents better reconstruction performance than other greedy pursuit algorithms. However, SAMP still suffers from being sensitive to the step size selection at high sub-sampling ratios. To solve this problem, this paper proposes a constrained backtracking matching pursuit (CBMP) algorithm for image reconstruction. The composite strategy, including two kinds of constraints, effectively controls the increment of the estimated sparsity level at different stages and accurately estimates the true support set of images. Based on the relationship analysis between the signal and measurement, an energy criterion is also proposed as a constraint. At the same time, the four-to-one rule is improved as an extra constraint. Comprehensive experimental results demonstrate that the proposed CBMP yields better performance and further stability than other greedy pursuit algorithms for image reconstruction.
Highlights
Image reconstruction is a significant application of multimedia signal processing.Compressed sensing (CS) is a technique that reconstructs sparse, compressible signals from under-determined random linear measurements
The same initial step size was used by constrained backtracking matching pursuit (CBMP), Sparsity adaptive matching pursuit (SAMP), and improved generalized sparsity adaptive matching pursuit (IGSAMP)
IGSAMP, the reconstruction results shown in their simulation experiments [23,26]
Summary
Image reconstruction is a significant application of multimedia signal processing. Compressed sensing (CS) is a technique that reconstructs sparse, compressible signals from under-determined random linear measurements. The basis pursuit (BP) algorithm is typically used for convex optimization, but its l1 norm-based cost function is sometimes not differentiable It involves high computational complexity, limiting its practical applications [13,14,15]. The improved generalized sparsity adaptive matching pursuit (IGSAMP) algorithm has been proposed This algorithm uses a nonlinear step size to approximate the sparsity level, and only a small initial step size can be selected. To improve the reconstruction performance of the sparsity adaptive matching pursuit algorithm and make it less sensitive to the step size, we propose a compositely constrained backtracking matching pursuit (CBMP) algorithm for image reconstruction. (4) The proposed algorithm can achieve satisfactory reconstruction performance and overcome the sensitivity to step size
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