Compressed Sensing MRI with Walsh Transform-based Sparsity Basis

The choice of sparsity bases plays a crucial role to reconstruct high-quality MR images from heavily under-sampled k-space signals. Traditionally, the Wavelet transform and the Total Variation (TV) are used as the sparsity bases. In this study, a novel sparsity basis, based on a two-dimensional Walsh transform, is proposed to sparsify the MR image. The basic theory of the Walsh transform-based CS-MRI is explained and the proposed technique is validated with experiments. Three different types of MR images are used to test the proposed method performance in terms of reconstruction accuracy. The results show that the proposed Walsh trans form-based sparsity basis is capable of reconstructing MRI images with a higher fidelity than the traditional Wavelet trans form-based sparsity basis using a similar running time.