Filter-based compressed sensing MRI reconstruction

Compressed sensing (CS) enables to reconstruct MR images from highly undersampled k-space data by exploiting the sparsity which is implicit in the images. In this article, an MR image ρ as a combination of a high-frequency component ρHP and a low-frequency component ρLP through a pair of filters has been proposed to express. Since ρHP exhibits a sparser representation in the wavelet transform domain, reconstructing ρHP and ρLP separately yields a better result than reconstructing ρ directly. Two parameters, normalized sparsity (NS) and power ratio (PR), are defined to design the filters, that is, the high-pass filter H_HP and the low-pass filter H_LP. H_HP is applied to pick out high-frequency k-space data for the reconstruction of high-frequency image (Formula presented.) while H_LP is used for filtering (Formula presented.), which is reconstructed from the entire undersampled k-space data to obtain the low-frequency reconstruction (Formula presented.). Summing (Formula presented.) and (Formula presented.) leads to the final reconstruction of ρ. Experimental results demonstrate that the proposed method outperforms the conventional CS-MRI method. It provides 2–4 dB improvement in peak signal to noise ratio (PSNR) value and preserves more edges and details in the images.