Tomographic image reconstruction from limited-view projections with Wiener filtered focuss algorithm

In tomographic image reconstruction from limited-view projections the underlying inverse problem is ill-posed with the rank-deficient system matrix. The minimal-norm least squares solution may considerably differs from the true solution, and hence a priori knowledge is needed to improve the reconstruction. In our approach, we assume that the true image presents sparse features with uniform spacial smoothness. The sparsity constraints are imposed with the lscrp diversity measure that is minimized with the FOCUSS algorithm. The spacial smoothness is enforced with the adaptive Wiener noise removing implemented in each FOCUSS iterations. The simulation results demonstrate the benefits of the proposed approach.

[1]  Jorge Herbert de Lira,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[2]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[3]  Joel A. Tropp,et al.  Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit , 2006, Signal Process..

[5]  P. Lancaster,et al.  The structure of some matrices arising in tomography , 1990 .

[6]  Aydogan Ozcan,et al.  Speckle reduction in optical coherence tomography images using digital filtering. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  Andrzej Cichocki,et al.  Efficient extraction of evoked potentials by combination of Wiener filtering and subspace methods , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[8]  Bhaskar D. Rao,et al.  Subset selection in noise based on diversity measure minimization , 2003, IEEE Trans. Signal Process..

[9]  R. Zdunek,et al.  Electromagnetic geotomography-selection of measuring frequency , 2005, IEEE Sensors Journal.

[10]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

[11]  Joseph F. Murray,et al.  Learning Sparse Overcomplete Codes for Images , 2006, J. VLSI Signal Process..

[12]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[13]  Fusheng Yang,et al.  Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction , 2005, IEEE Transactions on Biomedical Engineering.

[14]  Yoshinori Funama,et al.  Reduction of artifacts in degraded CT image by adaptive Wiener filter , 2002 .

[15]  L. Karlovitz.  Construction of nearest points in the Lp, p even, and L∞ norms. I , 1970 .

[16]  Kwang Suk Park,et al.  Regularized FOCUSS algorithm for EEG/MEG source imaging , 2004, The 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.