Self-adjusted regularization ratio for Robust Compressed Sensing

Introduction Minimizing the total Variation (TV) norm term in conjunction with a fidelity term has been effectively applied to Magnetic Resonance (MR) image reconstruction with partially acquired data [1, 3]. However, an inappropriate ratio, determined by the regularization parameter, between these two terms may result in either residual artifact or reduced spatial resolution. The optimization of the predefined regularization parameter is not trivial. This work aims to make this framework more robust to the choice of the regularization parameter. A self-adjustment technique is proposed in this work to automatically optimize the ratio between these two terms. Using compressed sensing (CS) [1] as an example, experiments with both phantom and in vivo data sets demonstrated that the proposed method made the regularized reconstruction framework less sensitive to the choice of regularization parameter. This work dramatically reduces the difficulty of parameter decision and increases the practicability of regularized reconstruction techniques. Theory Let X be the partially acquired MR data; I be the reconstructed image; Ω be the image domain; ∇ be the gradient operator; MR(·) be MR