Projection reconstruction MR imaging using FOCUSS

Abstract

The focal underdetermined system solver (FOCUSS) was originally designed to obtain sparse solutions by successively solving quadratic optimization problems. This article adapts FOCUSS for a projection reconstruction MR imaging problem to obtain high resolution reconstructions from angular undersampled radial k -space data. We show that FOCUSS is effective for projection reconstruction MRI, since medical images are usually sparse in some sense and the center region of the undersampled radial k -space samples still provides a low resolution, yet meaningful, image essential for the convergence of FOCUSS. Projection reconstruction (PR) with radial k-space trajectory was the first MRI k-space trajectory in MR history (1). However, cartesian k-space trajectory has replaced PR, mainly because of artifacts of PR that are related to B 0 inhomogeneity and to gradient nonlinearity (2). However, recent advances in MR hardware technology have overcome problems related to B 0 inhomogeneity and gradient nonlinearity, and interest in PR has thus been revived. PR has many advantages over the conventional cartesian k-space trajectory (3). Since no phase-encoding gradient is used, PR has a shorter minimum TE, which has made PR particularly desirable for imaging very short T 2 nuclei (3-5). Another advantage of PR is its robustness to the motion artifacts from flow or respiration. One important example is the reduction of motion artifacts in a diffusionweighted MRI (6,7). Furthermore, the aliasing artifacts from radial under-sampling usually appear as streaks, which are visually less distracting than the wrap-around artifacts obtained with cartesian under-sampling.One of the disadvantages of PR is the increased scan time involved if the Nyquist sampling criterion needs to be satisfied. More specifically, the number of radial lines N s required to satisfy the Nyquist criterion is given by (3):where L is the field-of-view (FOV), and k max is the maximum k-space radius. Usually, the number of radial lines acquired by PR is about 57% larger than the number of k-space lines acquired on a cartesian grid, which results in the increased scan time (3). If streak aliasing artifacts can be tolerated in an application, the scan time can be reduced by using angular undersampling. One such undersampled PR application is contrast-enhanced vascular imaging (8).Because of the properties of PR, if the contrast enhanced vessels are located at the center of the FOV, the undersampling aliasing artifacts appear as streaks near the periphery of the FOV and usually do not interfere with vessels located at the center of FOV. Hence, this application of PR for angiography has been a success (8).Rather than tolerating the angular aliasing artifacts, however, the main goal of our research is to develop a novel reconstruction algorithm with minimal angular aliasing. The bases of such a novel algorithm are the following two observations: (a) most medical imaging is sparse in some sense, and (b) the under-sampled PR still provides a meaningful low resolution imag...

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