Cargando…

Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images

This work addresses the problem of recovering multi-echo T1 or T2 weighted images from their partial K-space scans. Recent studies have shown that the best results are obtained when all the multi-echo images are reconstructed by simultaneously exploiting their intra-image spatial redundancy and inte...

Descripción completa

Detalles Bibliográficos
Autores principales: Majumdar, Angshul, Ward, Rabab
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Molecular Diversity Preservation International (MDPI) 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658782/
https://www.ncbi.nlm.nih.gov/pubmed/23519348
http://dx.doi.org/10.3390/s130303902
_version_ 1782270333582049280
author Majumdar, Angshul
Ward, Rabab
author_facet Majumdar, Angshul
Ward, Rabab
author_sort Majumdar, Angshul
collection PubMed
description This work addresses the problem of recovering multi-echo T1 or T2 weighted images from their partial K-space scans. Recent studies have shown that the best results are obtained when all the multi-echo images are reconstructed by simultaneously exploiting their intra-image spatial redundancy and inter-echo correlation. The aforesaid studies either stack the vectorised images (formed by row or columns concatenation) as columns of a Multiple Measurement Vector (MMV) matrix or concatenate them as a long vector. Owing to the inter-image correlation, the thus formed MMV matrix or the long concatenated vector is row-sparse or group-sparse respectively in a transform domain (wavelets). Consequently the reconstruction problem was formulated as a row-sparse MMV recovery or a group-sparse vector recovery. In this work we show that when the multi-echo images are arranged in the MMV form, the thus formed matrix is low-rank. We show that better reconstruction accuracy can be obtained when the information about rank-deficiency is incorporated into the row/group sparse recovery problem. Mathematically, this leads to a constrained optimization problem where the objective function promotes the signal's groups-sparsity as well as its rank-deficiency; the objective function is minimized subject to data fidelity constraints. The experiments were carried out on ex vivo and in vivo T2 weighted images of a rat's spinal cord. Results show that this method yields considerably superior results than state-of-the-art reconstruction techniques.
format Online
Article
Text
id pubmed-3658782
institution National Center for Biotechnology Information
language English
publishDate 2013
publisher Molecular Diversity Preservation International (MDPI)
record_format MEDLINE/PubMed
spelling pubmed-36587822013-05-30 Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images Majumdar, Angshul Ward, Rabab Sensors (Basel) Communication This work addresses the problem of recovering multi-echo T1 or T2 weighted images from their partial K-space scans. Recent studies have shown that the best results are obtained when all the multi-echo images are reconstructed by simultaneously exploiting their intra-image spatial redundancy and inter-echo correlation. The aforesaid studies either stack the vectorised images (formed by row or columns concatenation) as columns of a Multiple Measurement Vector (MMV) matrix or concatenate them as a long vector. Owing to the inter-image correlation, the thus formed MMV matrix or the long concatenated vector is row-sparse or group-sparse respectively in a transform domain (wavelets). Consequently the reconstruction problem was formulated as a row-sparse MMV recovery or a group-sparse vector recovery. In this work we show that when the multi-echo images are arranged in the MMV form, the thus formed matrix is low-rank. We show that better reconstruction accuracy can be obtained when the information about rank-deficiency is incorporated into the row/group sparse recovery problem. Mathematically, this leads to a constrained optimization problem where the objective function promotes the signal's groups-sparsity as well as its rank-deficiency; the objective function is minimized subject to data fidelity constraints. The experiments were carried out on ex vivo and in vivo T2 weighted images of a rat's spinal cord. Results show that this method yields considerably superior results than state-of-the-art reconstruction techniques. Molecular Diversity Preservation International (MDPI) 2013-03-20 /pmc/articles/PMC3658782/ /pubmed/23519348 http://dx.doi.org/10.3390/s130303902 Text en © 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
spellingShingle Communication
Majumdar, Angshul
Ward, Rabab
Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images
title Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images
title_full Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images
title_fullStr Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images
title_full_unstemmed Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images
title_short Rank Awareness in Group-Sparse Recovery of Multi-Echo MR Images
title_sort rank awareness in group-sparse recovery of multi-echo mr images
topic Communication
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658782/
https://www.ncbi.nlm.nih.gov/pubmed/23519348
http://dx.doi.org/10.3390/s130303902
work_keys_str_mv AT majumdarangshul rankawarenessingroupsparserecoveryofmultiechomrimages
AT wardrabab rankawarenessingroupsparserecoveryofmultiechomrimages