Weighted wavelet tree sparsity regularization for compressed sensing magnetic resonance image reconstruction

Abstract

Compressed sensing in magnetic resonance imaging (CS-MRI) improves the MRI scan time by acquiring only a few k-space samples and then reconstructs the image using a nonlinear procedure from the highly undersampled measurements. Besides the standard wavelet sparsity, MR images are also found to exhibit tree sparsity across various scales of the wavelet decomposition which are generally modeled as overlapping group sparsity. In this chapter, we propose a novel iteratively weighted wavelet tree sparsity based CS-MRI reconstruction technique to estimate MR images from highly undersampled Fourier measurements. Simulations on various real MR images show that the proposed technique offers significant improvements compared to the state-of-the-art either in terms of visual quality or k-space measurements with the same reconstruction time.