A Fast Linearized Alternating Minimization Algorithm for Constrained High-Order Total Variation Regularized Compressive Sensing

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.