Optimal k-space sampling in MRSI for images with a limited region of support

Magnetic resonance spectroscopic imaging requires a great deal of time to g ather the data necessary to achieve satisfactory resolution. When the image has a limited region of support (ROS), it is possible to reconstruct the i mage from a subset of k-space samples. Therefore, we desire to choose the b est possible combination of a small number of k-space samples to guarantee the quality of the reconstructed image. Sequential forward selection (SFS) is appealing as an optimization method because the previously selected samp le can be observed while the nest sample is selected. However, when the num ber of selected k-space samples is less than the number of unknowns at the beginning of the selection process, the optimality criterion is undefined a nd the resulting SFS algorithm cannot be used, In this paper, we present a modified form of the criterion that overcomes this problem and develop an S FS algorithm for the new criterion. Then we develop an efficient computatio nal strategy for this algorithm as well as for the standard SFS algorithm. The combined algorithm efficiently selects a reduced set of k-space samples from which the ROS can be reconstructed with minimal noise amplification.