Compressed Sensing for Thoracic MRI with Partial Random Circulant Matrices

Windra Swastika, Hideaki Haneishi


The use of circulant matrix as the sensing matrix in compressed sensing (CS) scheme has recently been proposed to overcome the limitation of random or partial Fourier matrices. Aside from reducing computational complexity, the use of circulant matrix for magnetic resonance (MR) image offers the feasibility in hardware implementations. This paper presents the simulation of compressed sensing for thoracic MR imaging with circulant matrix as the sensing matrix. The comparisons of reconstruction of three different type MR images using circulant matrix are investigated in term of number of samples, number of iteration and signal to noise ratio (SNR). The simulation results showed that circulant matrix works efficiently for encoding the MR image of respiratory organ, especially for smooth and sparse image in spatial domain.

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N Yudistira, D Daman. Issues and Problems in Brain Magnetic Resonance Imaging: An Overview. TELKOMNIKA. 2008; 6(1): 57-64.

DL Donoho. Compressed Sensing. IEEE Transactions on Information Theory. 2006; 52 (4): 1289–1306

E Candés, J Romberg, T Tao. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. Information Theory IEEE Transactions. 2006; 52(2): 489-509.

R Van de Walle, I Lemahieu, E Achten. Magnetic Resonance Imaging and the Reduction of Motion Artifacts: Review of the Principles. Technology and Health Care. 1997; 5(6):419-435.

M Lustig, D Donoho, JM Pauly. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 2007; 58(6): 1182-1195.

SKP Pruessmann. Encoding and reconstruction in parallel MRI. NMR in Biomedicine. 2006; 19(3): 288–299.

E Candés, T Tao. Decoding by linear programming. IEEE Transaction on Information Theory. 2005; 51: 4203-4215.

E Candés, JK Romberg, T Tao. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 2006; 59(8):1207–1223.

TT Do, TD Tran, L Gan. Fast compressive sampling with structurally random matrices. Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing. 2008: 3369-3372.

H Rauhut, J Romberg, J Tropp. Restricted isometries for partial random circulant matrices. Arxiv preprint. 2010; arXiv:1010.1847

J Tropp, M Wakin, M Duarte, D Baron, R Baraniuk. Random filters for compressive sampling and reconstruction. Int. Conf. Acoustics, Speech, and Signal Processing. 2006; 3: 872–875.

W Yin, SP Morgan, J Yang, Y Zhang. Practical compressive sensing with toeplitz and circulant matrices. 2010; Rice University CAAM Technical Report TR10-01.

M Nasri, A Helali, H Sghaier, H Maaref. Efficient JPEG 2000 Image Compression Scheme for Multihop Wireless Networks. TELKOMNIKA. 2011; 9(2): 311-318.

A Alfiansyah. A Unified Engergy Approach for B-Spline Snake in Medical Image Segmentation. TELKOMNIKA. 2010; 8(2): 175-186. Practical Compressive Sensing with Toeplitz and Circulant Matrices. Last access: Nov 24, 2011; 14:27pm.


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