Smoothly clipped absolute deviation (SCAD) regularization for compressed sensing MRI using an augmented Lagrangian scheme

Abstract

Objective: Compressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l1 norm while approaching an l0 norm .
Results: It was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l1-based counterpart.
Conclusion: The SCAD regularization improves the performance of l1-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI.