Compressed sensing MRI by two-dimensional wavelet filter banks

How to speed up the scanning process is the bottleneck problem of magnetic resonance imaging (MRI). As a newly developed mathematical framework of signal sampling and recovery, compressed sensing (CS) provides a solution to this problem because of its potential of reconstructing MR images from fewer samples. Recent work has demonstrated successful application of CS to MRI. However, the frequently used sparsifying transform is the traditional discrete wavelet transform, which has shortcomings, such as oscillations, lack of directionality and shift variance. This paper implements compressed sensing MRI reconstruction based on a new kind of two-dimensional wavelet filter banks which has improved directional selectivity and approximate shift invariance. Our experiments show that the method can significantly reduce aliasing and achieve higher peak signal to noise ratio (PSNR).