Compressed Sensing MRI Reconstruction Algorithm Based on Contourlet Transform and Alternating Direction Method

Zhenyu Hu,Lai Wang,Qiuye Wang,Jian Zou,Yuanqing Hu,Congcong Ming

doi:10.1155/2015/175231

Zhenyu Hu, Lai Wang + Show 4 more

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https://doi.org/10.1155/2015/175231

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Abstract

Compressed sensing (CS) based methods have recently been used to reconstruct magnetic resonance (MR) images from undersampled measurements, which is known as CS-MRI. In traditional CS-MRI, wavelet transform can hardly capture the information of image curves and edges. In this paper, we present a new CS-MRI reconstruction algorithm based on contourlet transform and alternating direction method (ADM). The MR images are firstly represented by contourlet transform, which can describe the images’ curves and edges fully and accurately. Then the MR images are reconstructed by ADM, which is an effective CS reconstruction method. Numerical results validate the superior performance of the proposed algorithm in terms of reconstruction accuracy and computation time.

Highlights

Compressed sensing (CS) is a new sampling and compression theory
We present a new CS-MRI reconstruction algorithm based on contourlet transform and alternating direction method (ADM)
We present alternating direction method for problem (3) as Algorithm 1

Summary

Introduction

CS is a new sampling and compression theory It utilizes the sparseness of a signal in a particular domain and can reconstruct the signal from significantly fewer samples than Nyquist sampling, which has been the fundamental principle in signal processing for many years [1,2,3]. In MRI reconstruction, the MR images themselves are not sparse but have sparse representations in some transform domains. As the limitations of direction, wavelet transform can hardly capture the information of image curves and edges fully and accurately. We present a new CS-MRI reconstruction algorithm based on contourlet transform and ADM. The proposed algorithm can recover the curves and edges of a MR image more precisely and suit large-scale MRI reconstruction. The organization of the rest of this paper is as follows: in Section 2, we first introduce CS-MRI model briefly and present our new algorithm.

ADM for Contourlet-Based CS-MRI

Numerical Experiments

Conclusion