Super Resolution Image Reconstruction Through Bregman Iteration Using Morphologic Regularization

Multiscale morphological operators are studied extensively in the literature for image processing and feature extraction purposes. In this paper, we model a nonlinear regularization method based on multiscale morphology for edge-preserving super resolution (SR) image reconstruction. We formulate SR image reconstruction as a deblurring problem and then solve the inverse problem using Bregman iterations. The proposed algorithm can suppress inherent noise generated during low-resolution image formation as well as during SR image estimation efficiently. Experimental results show the effectiveness of the proposed regularization and reconstruction method for SR image.

[1]  Michael Elad,et al.  Generalizing the Nonlocal-Means to Super-Resolution Reconstruction , 2009, IEEE Transactions on Image Processing.

[2]  Sung-Jea Ko,et al.  Center weighted median filters and their applications to image enhancement , 1991 .

[3]  Michael Elad,et al.  Example-Based Regularization Deployed to Super-Resolution Reconstruction of a Single Image , 2009, Comput. J..

[4]  Peyman Milanfar,et al.  A computationally efficient superresolution image reconstruction algorithm , 2001, IEEE Trans. Image Process..

[5]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[6]  H. Wu,et al.  Adaptive impulse detection using center-weighted median filters , 2001, IEEE Signal Processing Letters.

[7]  Nirmal K. Bose,et al.  Recursive reconstruction of high resolution image from noisy undersampled multiframes , 1990, IEEE Trans. Acoust. Speech Signal Process..

[8]  Kwang In Kim,et al.  Single-Image Super-Resolution Using Sparse Regression and Natural Image Prior , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Michael Elad,et al.  Super-Resolution Without Explicit Subpixel Motion Estimation , 2009, IEEE Transactions on Image Processing.

[10]  Stanley Osher,et al.  Image Super-Resolution by TV-Regularization and Bregman Iteration , 2008, J. Sci. Comput..

[11]  Michael Elad,et al.  Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images , 1997, IEEE Trans. Image Process..

[12]  N. K. Bose,et al.  High resolution image formation from low resolution frames using Delaunay triangulation , 2002, IEEE Trans. Image Process..

[13]  Liangpei Zhang,et al.  A MAP Approach for Joint Motion Estimation, Segmentation, and Super Resolution , 2007, IEEE Transactions on Image Processing.

[14]  H Stark,et al.  High-resolution image recovery from image-plane arrays, using convex projections. , 1989, Journal of the Optical Society of America. A, Optics and image science.

[15]  Wotao Yin,et al.  Bregman Iterative Algorithms for (cid:2) 1 -Minimization with Applications to Compressed Sensing ∗ , 2008 .

[16]  Bin Dong,et al.  Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising , 2011, ArXiv.

[17]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[18]  Michael Elad,et al.  Fast and robust multiframe super resolution , 2004, IEEE Transactions on Image Processing.

[19]  Michael Elad,et al.  On the bilateral filter and ways to improve it , 2002 .

[20]  Yücel Altunbasak,et al.  Artifact reduction for set theoretic super resolution image reconstruction with edge adaptive constraints and higher-order interpolants , 2001, IEEE Trans. Image Process..

[21]  Wotao Yin,et al.  An Iterative Regularization Method for Total Variation-Based Image Restoration , 2005, Multiscale Model. Simul..

[22]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[23]  Aggelos K. Katsaggelos,et al.  Reconstruction of a high-resolution image by simultaneous registration, restoration, and interpolation of low-resolution images , 1995, Proceedings., International Conference on Image Processing.

[24]  L. He,et al.  MR Image Reconstruction from Sparse Radial Samples Using Bregman Iteration , 2006 .

[25]  Xuelong Li,et al.  A multi-frame image super-resolution method , 2010, Signal Process..

[26]  Brendt Wohlberg,et al.  Efficient Minimization Method for a Generalized Total Variation Functional , 2009, IEEE Transactions on Image Processing.

[27]  Luc Vincent,et al.  Morphological grayscale reconstruction in image analysis: applications and efficient algorithms , 1993, IEEE Trans. Image Process..

[28]  Mei Han,et al.  Soft Edge Smoothness Prior for Alpha Channel Super Resolution , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[29]  Bhabatosh Chanda,et al.  Enhancing effective depth-of-field by image fusion using mathematical morphology , 2006, Image Vis. Comput..

[30]  Michal Irani,et al.  Improving resolution by image registration , 1991, CVGIP Graph. Model. Image Process..

[31]  EladMichael,et al.  Example-Based Regularization Deployed to Super-Resolution Reconstruction of a Single Image , 2009 .

[32]  Michael Elad,et al.  On the origin of the bilateral filter and ways to improve it , 2002, IEEE Trans. Image Process..

[33]  Michal Irani,et al.  Super-resolution from a single image , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[34]  Peyman Milanfar,et al.  An efficient wavelet-based algorithm for image superresolution , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[35]  GoldfarbDonald,et al.  Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing , 2008 .

[36]  Gemma Piella,et al.  A general framework for multiresolution image fusion: from pixels to regions , 2003, Inf. Fusion.

[37]  Petros Maragos,et al.  Evolution equations for continuous-scale morphological filtering , 1994, IEEE Trans. Signal Process..

[38]  Jian-Feng Cai,et al.  Linearized Bregman iterations for compressed sensing , 2009, Math. Comput..

[39]  Bhabatosh Chanda,et al.  Multiscale morphological segmentation of gray-scale images , 2003, IEEE Trans. Image Process..

[40]  S. Mukhopadhyay,et al.  An edge preserving noise smoothing technique using multiscale morphology , 2002, Signal Process..

[41]  Michael Elad,et al.  A fast super-resolution reconstruction algorithm for pure translational motion and common space-invariant blur , 2001, IEEE Trans. Image Process..

[42]  William T. Freeman,et al.  Example-Based Super-Resolution , 2002, IEEE Computer Graphics and Applications.

[43]  Thomas S. Huang,et al.  Image Super-Resolution Via Sparse Representation , 2010, IEEE Transactions on Image Processing.

[44]  Edmund Y. Lam,et al.  Application of Tikhonov Regularization to Super-Resolution Reconstruction of Brain MRI Images , 2007, MIMI.

[45]  Patrick L. Combettes,et al.  Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..

[46]  Pierre Soille,et al.  Morphological Image Analysis: Principles and Applications , 2003 .

[47]  J. Moreau.  Fonctions convexes duales et points proximaux dans un espace hilbertien , 1962 .

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

[49]  Lei Zhang,et al.  Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization , 2010, IEEE Transactions on Image Processing.

[50]  Yin Zhang,et al.  Fixed-Point Continuation for l1-Minimization: Methodology and Convergence , 2008, SIAM J. Optim..

[51]  Liang Xiao,et al.  A Super-resolution Reconstruction via Local and Contextual Information Driven Partial Differential Equations , 2007, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007).

[52]  Youji Iiguni,et al.  Morphological image regularization with a smoothness criterion of structuring elements , 2010, 2010 10th International Symposium on Communications and Information Technologies.

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