Abstract
In this paper, we propose a new high-order total variation regularized model with box constraint for image compressive sensing reconstruction. Because of the separable structure of this model, we can easily decompose into three subproblems by splitting the augmented Lagrangian function. To effectively solve the proposed new model, a fast alternating minimization method with accelerated technique is presented. Moreover, the proposed method applies a linearized strategy for quadratic terms to get the closed-form solution and reduce the computation cost. Numerical experiments show that our proposed model can get better performance than several current state-of-the-art methods in terms of signal to noise ratio (SNR) and visual perception.
Highlights
Recently, compressive sensing as an emerging methodology in digital signal processing was proposed by Donoho [1], Candés et al [2], and Romberg [3] and has drawn extensive attentions from different research fields
The compressive sensing theory demonstrates that sparse signal/image reconstruction can be achieved with only a few or incomplete measurements
Considering its powerful handling capacity, compressive sensing theory has come into use for sensing image processing, magnetic resonance imaging [4]–[7]
Summary
Compressive sensing as an emerging methodology in digital signal processing was proposed by Donoho [1], Candés et al [2], and Romberg [3] and has drawn extensive attentions from different research fields. B. Hao et al.: Fast Linearized Alternating Minimization Algorithm for Constrained High-Order TV Regularized Compressive Sensing method, gradient projection method, partial differential equation (PDE) based method, alternating minimization method, see for instance, [9]–[16] and references therein. Since A is random projection matrix in [16], the computational burden of using the above method to solve the problem will be costly To avoid this situation, the authors use the linear expansion technique to propose a new alternating minimization algorithm (FTVCS) to solve model (2). In order to eliminate the staircase effects while preserving the edges well in the restored image, some high-order variational models [27]–[31] are introduced, which include the second order TV regularization terms.
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