An Adaptive Algorithm for Compressively Sampled MR Image Reconstruction Using Projections onto \(l_{p}\)-Ball
- Authors: Kaleem M.1, Qureshi M.1, Omer H.1
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Affiliations:
- COMSATS Institute of Information Technology
- Issue: Vol 47, No 4 (2016)
- Pages: 415-428
- Section: Article
- URL: https://journals.rcsi.science/0937-9347/article/view/247452
- DOI: https://doi.org/10.1007/s00723-016-0761-0
- ID: 247452
Cite item
Abstract
Compressed sensing (CS) is an emerging technique for magnetic resonance imaging (MRI) reconstruction from randomly under-sampled k-space data. CS utilizes the reconstruction of MR images in the transform domain using any non-linear recovery algorithm. The missing data in the \(k\)-space are conventionally estimated based on the minimization of the objective function using \(l_{1} - l_{2}\) norms. In this paper, we propose a new CS-MRI approach called tangent-vector-based gradient algorithm for the reconstruction of compressively under-sampled MR images. The proposed method utilizes a unit-norm constraint adaptive algorithm for compressively sampled data. This algorithm has a simple design and has shown good convergence behavior. A comparison between the proposed algorithm and conjugate gradient (CG) is discussed. Quantitative analyses in terms of artifact power, normalized mean square error and peak signal-to-noise ratio are provided to illustrate the effectiveness of the proposed algorithm. In essence, the proposed algorithm improves the minimization of the quadratic cost function by imposing a sparsity inducing \(l_{p}\)-norm constraint. The results show that the proposed algorithm exploits the sparsity in the acquired under-sampled MRI data effectively and exhibits improved reconstruction results both qualitatively and quantitatively as compared to CG.
About the authors
Muhammad Kaleem
COMSATS Institute of Information Technology
Author for correspondence.
Email: kaleem.arfeen@gmail.com
Pakistan, Islamabad
Mahmood Qureshi
COMSATS Institute of Information Technology
Email: kaleem.arfeen@gmail.com
Pakistan, Islamabad
Hammad Omer
COMSATS Institute of Information Technology
Email: kaleem.arfeen@gmail.com
Pakistan, Islamabad