The Magic of Nonlocal Perona–Malik Diffusion

In this letter, we show that it is possible to obtain perfect reconstruction of the 256 X 256 phantom image from only 8 radial lines in the Fourier domain by a nonlocal extension of Perona-Malik diffusion.

[1]  Karen O. Egiazarian,et al.  Compressed Sensing Image Reconstruction Via Recursive Spatially Adaptive Filtering , 2007, ICIP.

[2]  K. Rose Deterministic annealing for clustering, compression, classification, regression, and related optimization problems , 1998, Proc. IEEE.

[3]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[4]  Guillermo Sapiro,et al.  Robust anisotropic diffusion , 1998, IEEE Trans. Image Process..

[5]  Guy Gilboa,et al.  Nonlocal Operators with Applications to Image Processing , 2008, Multiscale Model. Simul..

[6]  Dante C. Youla,et al.  Generalized Image Restoration by the Method of Alternating Orthogonal Projections , 1978 .

[7]  G. Sapiro,et al.  Geometric partial differential equations and image analysis [Book Reviews] , 2001, IEEE Transactions on Medical Imaging.

[8]  Satyanad Kichenassamy,et al.  The Perona-Malik Paradox , 1997, SIAM J. Appl. Math..

[9]  Daniel Cohen-Or,et al.  Fragment-based image completion , 2003, ACM Trans. Graph..

[10]  Xavier Bresson,et al.  Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction , 2010, SIAM J. Imaging Sci..

[11]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Armando Manduca,et al.  Highly Undersampled Magnetic Resonance Image Reconstruction via Homotopic $\ell_{0}$ -Minimization , 2009, IEEE Transactions on Medical Imaging.

[13]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[14]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[15]  Rick Chartrand,et al.  Exact Reconstruction of Sparse Signals via Nonconvex Minimization , 2007, IEEE Signal Processing Letters.