A novel algorithm for the reduction of undersampling artefacts in magnetic resonance images

Abstract

An innovative algorithm is presented which is effective in reducing the truncation artefacts occurring in magnetic resonance images due to missing k-space samples. The algorithm works first by filling the incomplete matrix of coefficients with zeroes and then adjusting, by an iterative process, the missing coefficients by performing a reduction of the undersampling artefacts. Then, this set of coefficients is used as a basis for a superresolution algorithm that estimates the missing coefficients by modeling the data as a linear combination of increasing and decreasing exponential functions using Prony's method. In fact, the Prony's method consists of the interpolation of a given data set with a sum of exponential functions: the MRI signals can be well represented as a sum of exponential functions and the missing data can be extrapolated by this representation. The algorithm has been proven to perform better than either a simple algorithm, which detects and then reduces the undersampling artefacts, or an algorithm that models the measured data with approximation functions. The presented algorithm is quite simple and is applicable both to missing rows (phase-frequency acquisitions) and to radial-missing angle (acquisition from projections) undersampling. Experimental results are reported; comparisons, made between the results obtained using the presented algorithm and the alternative methods described above, clearly demonstrate the superiority of the algorithm.