Adaptive variable density sampling based on Knapsack problem for fast MRI

This paper presents a novel heuristic approach to generate a variable density sampling (VDS) pattern for fast MRI data acquisition, based on the principle of Knapsack problem. MR images are known to exhibit weak sparsity in Fourier domain. This sparsity has been exploited to devise faster k-space sampling schemes by acquiring lesser samples while using Compressed Sensing reconstruction techniques to reconstruct high quality MR images. The entire range of distribution of the magnitude of fc-space is divided into fixed/variable bin widths and draw samples from these bins according to a cost criterion satisfying the undersampling factor. This will facilitate sampling the k-space coefficients by preserving the energy content for the desired undersampling factor and do away with the deterministic central region sampling resulting in a VDS method with a correlation to the magnitude spectrum of the reference image scan. Knapsack principle is used to select the relevant bins. The method is also devoid of parameter tuning, yielding significant good results at both the lower and higher under sampling ratios.