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 HHP and the low‐pass filter HLP. HHP is applied to pick out high‐frequency k‐space data for the reconstruction of high‐frequency image ρ̂HP ; while HLP is used for filtering ρ′̂ , which is reconstructed from the entire undersampled k‐space data to obtain the low‐frequency reconstruction ρ̂LP . Summing ρ̂HP and ρ̂LP 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. © 2016 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 26, 173–178, 2016