Multispectral super-resolution of tropical cyclone imagery using sparsity-based approaches

ABSTRACT An aperture synthesis system produces ringing at sharp edges and other transitions in the observed field. In this article, we have developed an efficient multispectral deconvolution method, based on the Split Bregman total variation minimization technique, and it was successful in reducing image ringing, blurring, and distortion, while sharpening the image and preserving the information content. We also present a multispectral multi-frame super-resolution method that is robust to image noise and noise in the point spread function (PSF) and leads to additional improvements in spatial resolution. The methodologies are based on current research in sparse optimization and compressed sensing, which lead to unprecedented efficiencies in solving image reconstruction problems.

[1]  B. Mercier,et al.  A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .

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

[3]  R. Glowinski,et al.  Numerical Analysis of Variational Inequalities , 1981 .

[4]  Guy Gilboa,et al.  Nonlocal Linear Image Regularization and Supervised Segmentation , 2007, Multiscale Model. Simul..

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

[6]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[7]  J. Michalakes,et al.  Design of a next-generation regional weather research and forecast model. , 1999 .

[8]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

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

[10]  Jean-Michel Morel,et al.  A Review of Image Denoising Algorithms, with a New One , 2005, Multiscale Model. Simul..

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

[12]  Gabriel Peyré,et al.  Image Processing with Nonlocal Spectral Bases , 2008, Multiscale Model. Simul..

[13]  R. Glowinski,et al.  Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires , 1975 .

[14]  Stanley Osher,et al.  Deblurring and Denoising of Images by Nonlocal Functionals , 2005, Multiscale Model. Simul..

[15]  Luminita A. Vese,et al.  Variational multiframe restoration of images degraded by noisy (stochastic) blur kernels , 2013, J. Comput. Appl. Math..

[16]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[17]  Luminita A. Vese,et al.  Efficient Deconvolution and Super-Resolution Methods in Microwave Imagery , 2015, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[18]  Christopher Ruf,et al.  Initial Results of the Geostationary Synthetic Thinned Array Radiometer (GeoSTAR) Demonstrator Instrument , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[19]  Junfeng Yang,et al.  A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data , 2010, IEEE Journal of Selected Topics in Signal Processing.

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

[21]  Junfeng Yang,et al.  An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise , 2009, SIAM J. Sci. Comput..

[22]  Junfeng Yang,et al.  A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration , 2009, SIAM J. Imaging Sci..

[23]  Ronald R. Coifman,et al.  Regularization on Graphs with Function-adapted Diffusion Processes , 2008, J. Mach. Learn. Res..

[24]  Yin Zhang,et al.  A Fast Algorithm for Image Deblurring with Total Variation Regularization , 2007 .

[25]  Luminita A. Vese,et al.  Multiframe image restoration in the presence of noisy blur kernel , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[26]  Alan B. Tanner,et al.  Calibration of a synthetic aperture radiometer , 1993, IEEE Trans. Geosci. Remote. Sens..

[27]  Wotao Yin,et al.  Edge Guided Reconstruction for Compressive Imaging , 2012, SIAM J. Imaging Sci..

[28]  Xavier Bresson,et al.  Nonlocal Mumford-Shah Regularizers for Color Image Restoration , 2011, IEEE Transactions on Image Processing.

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

[30]  Stanley Osher,et al.  Image Recovery via Nonlocal Operators , 2010, J. Sci. Comput..

[31]  Xavier Bresson,et al.  Color Image Restoration Using Nonlocal Mumford-Shah Regularizers , 2009, EMMCVPR.