Non-convex greedy compressed sensing for phase contrast MRI

Introduction We propose a novel compressed sensing algorithm for Phase Contrast MRI(PC-MRI) to estimate blood flow velocities. Blood flow velocities provide clinically useful information such as pressure gradients and PC-MRI has become an established technique to measure them. In conventional PC-MRI, velocity information is computed by comparing the phases of the velocity-encoded image and the reference image without velocity encoding. This procedure requires multiple scans of the imaged object, which is time-intensive. For example, it takes about 20 minutes to cover a 3D volume of 16x12x6cm with a previously proposed PC-MRI sequence[1]. We have observed empirically that velocity encoding brings about phase changes only in blood vessel regions, which are sparse in the image domain[2]. Exploiting this sparse phase differences, we developed a non-convex greedy compressed sensing image reconstruction algorithm to accelerate the acquisition of velocity encoded images. Simulation results show that with random k-space sampling, our algorithm can perform well even with a high undersampling factor 15. We have also investigated an alternative convex optimization approach and compared its performance with our greedy algorithm. The simulation results show that our proposed greedy algorithm is more robust in high undersampling factors compared to the convex optimization method. Theory Let xref denote the reference image acquired without velocity encoding. The signal equation for the k-space data, y, of a velocity encoded object in the matrix-vector form can be modeled as ) ( , ] [ ] [ ref i i ref x e e x Diag F A A F y θ θ ⋅ = = ⋅ = where F is a undersampled Fourier encoding matrix, Diag(xref) is a diagonal matrix with entries