Translational-invariant dictionaries for compressed sensing in magnetic resonance imaging

A sparse representation is an essential part of compressed sensing (CS). The discrete wavelet transform has been widely used to sparsely represent magnetic resonance images for CS applications. Artifacts usually exist in CS reconstruction when the wavelet transform is used alone. In this work, we investigate improving the image reconstruction quality through redundant translational-invariant sparsifying transforms. Cycle spinning is used with the wavelet transform and overlapping patches are used with the discrete cosine transform to achieve translational invariance. Experimental results show significant improvement in artifact reduction when contrasted with non-translational invariant transforms.