MR Image Reconstruction with Convolutional Characteristic Constraint (CoCCo)

The problem of recovering an image from limited or sparsely sampled Fourier measurements occurs in the application of magnetic resonance imaging. To address this problem, we propose a novel MR image reconstruction method with convolutional characteristic constraints. We first estimate the convolutional characteristics using standard compressed sensing method in a parallel fashion. Then we use the recovered image characteristics to constrain the target image function. The image characteristics should either be sparser or of higher SNR than the original image to enable superior performance. In this work, we studied using thirteen kernels and experiments based on a brain data set were conducted. It is demonstrated that the proposed method outperforms the existing methods in terms of high quality imaging due to multiple characteristic constraints and the robustness to measurement noise.

I. Introduction

With proper discretization, the signal acquisition scheme for MRI can be mathematically expressed as:

$${\bf d} = {{\bf F}_u}\rho + {\bf n},\eqno{\hbox{(1)}}$$ where is the desired image function, represents the K-space measurements. and are the number of image pixels and measured data respectively. is the undersampled Fourier encoding matrix with . denotes the observation noise usually assumed to be complex Gaussian. The goal is to recover from .