Enhancing MR Image Reconstruction Using Block Dictionary Learning

Abstract

While representing a class of signals in term of sparsifying transform, it is better to use a adapted learned dictionary instead of using a predefined dictionary as proposed in the recent literature. With this improved method, one can represent the sparsest representation for the given set of signals. In order to ease the approximation, atoms of the learned dictionary can further be grouped together to make blocks inside the dictionary that act as a union of small number of subspaces. The block structure of a dictionary can be learned by exploiting the latent structure of the desired signals. Such type of block dictionary leads to block sparse representation of the given signals which can be good for reconstruction of the medical images. In this article, we suggest a framework for MRI reconstruction based upon block sparsifying transform (dictionary). Our technique develops automatic detection of underlying block structure of MR images given maximum block sizes. This is done by iteratively alternating between updating the block structure of the sparsifying transform (dictionary) and block-sparse representation of the MR images. Empirically it is shown that block-sparse representation performs better for recovery of the given MR image with minimum errors.

Keywords

• Compressed sensing (CS)
• sparsifying transforms
• magnetic resonance imaging (MRI)
• k-singular value decomposition (BLKSVD)%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> block <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">k</italic>-singular value decomposition (BLKSVD)