Wavelet-Based Sparse Reduced-Rank Regression for Hyperspectral Image Restoration

In this paper, a method called wavelet-based sparse reduced-rank regression (WSRRR) is proposed for hyperspectral image restoration. The method is based on minimizing a sparse regularization problem subject to an orthogonality constraint. A cyclic descent-type algorithm is derived for solving the minimization problem. For selecting the tuning parameters, we propose a method based on Stein's unbiased risk estimation. It is shown that the hyperspectral image can be restored using a few sparse components. The method is evaluated using signal-to-noise ratio and spectral angle distance for a simulated noisy data set and by classification accuracies for a real data set. Two different classifiers, namely, support vector machines and random forest, are used in this paper. The method is compared to other restoration methods, and it is shown that WSRRR outperforms them for the simulated noisy data set. It is also shown in the experiments on a real data set that WSRRR not only effectively removes noise but also maintains more fine features compared to other methods used. WSRRR also gives higher classification accuracies.

[1]  Salah Bourennane,et al.  Noise Removal From Hyperspectral Images by Multidimensional Filtering , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[2]  Johannes R. Sveinsson,et al.  Hyperspectral image denoising using 3D wavelets , 2012, 2012 IEEE International Geoscience and Remote Sensing Symposium.

[3]  Qi Wang,et al.  3-D nonlocal means filter with noise estimation for hyperspectral imagery denoising , 2012, 2012 IEEE International Geoscience and Remote Sensing Symposium.

[4]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[5]  Guillermo Sapiro,et al.  Non-local sparse models for image restoration , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[6]  Tao Lin,et al.  Hyperspectral Image Processing by Jointly Filtering Wavelet Component Tensor , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Guangyi Chen,et al.  Denoising of Hyperspectral Imagery Using Principal Component Analysis and Wavelet Shrinkage , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[8]  Marco Diani,et al.  Signal-Dependent Noise Modeling and Model Parameter Estimation in Hyperspectral Images , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[9]  Jennifer L. Dungan,et al.  Estimation of signal-to-noise: a new procedure applied to AVIRIS data , 1989 .

[10]  Xuelong Li,et al.  Image Super-Resolution With Sparse Neighbor Embedding , 2012, IEEE Transactions on Image Processing.

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

[12]  Adam Krzyzak,et al.  Denoising of Three Dimensional Data Cube Using Bivariate Wavelet Shrinking , 2010, ICIAR.

[13]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[14]  Guangyi Chen,et al.  Denoising of hyperspectral imagery by combining PCA with block-matching 3-D filtering , 2011 .

[15]  Thomas E. Nichols,et al.  Discovering genetic associations with high-dimensional neuroimaging phenotypes: A sparse reduced-rank regression approach , 2010, NeuroImage.

[16]  Dacheng Tao,et al.  Double Shrinking Sparse Dimension Reduction , 2013, IEEE Transactions on Image Processing.

[17]  Jon Atli Benediktsson,et al.  Advances in Spectral-Spatial Classification of Hyperspectral Images , 2013, Proceedings of the IEEE.

[18]  Liangpei Zhang,et al.  Hyperspectral Image Denoising Employing a Spectral–Spatial Adaptive Total Variation Model , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[19]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[20]  Karen O. Egiazarian,et al.  Image denoising with block-matching and 3D filtering , 2006, Electronic Imaging.

[21]  J. B. Lee,et al.  Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform , 1990 .

[22]  Michael Zibulevsky,et al.  Signal reconstruction in sensor arrays using sparse representations , 2006, Signal Process..

[23]  Levent Sendur,et al.  A bivariate shrinkage function for wavelet-based denoising , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[25]  Johannes R. Sveinsson,et al.  Hyperspectral Image Denoising Using First Order Spectral Roughness Penalty in Wavelet Domain , 2014, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[26]  Minchao Ye,et al.  Hyperspectral Imagery Restoration Using Nonlocal Spectral-Spatial Structured Sparse Representation With Noise Estimation , 2013, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[27]  Mário A. T. Figueiredo,et al.  Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors , 2009, Optical Engineering + Applications.

[28]  José M. Bioucas-Dias,et al.  Hyperspectral Subspace Identification , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[29]  G. Reinsel,et al.  Multivariate Reduced-Rank Regression: Theory and Applications , 1998 .

[30]  C. Stein Estimation of the Mean of a Multivariate Normal Distribution , 1981 .

[31]  Richard Baraniuk,et al.  The Dual-tree Complex Wavelet Transform , 2007 .

[32]  Jon Atli Benediktsson,et al.  A Novel Technique for Optimal Feature Selection in Attribute Profiles Based on Genetic Algorithms , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Joos Vandewalle,et al.  On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors , 2000, SIAM J. Matrix Anal. Appl..

[34]  Vivek K. Goyal,et al.  Denoising Hyperspectral Imagery and Recovering Junk Bands using Wavelets and Sparse Approximation , 2006, 2006 IEEE International Symposium on Geoscience and Remote Sensing.

[35]  Rémi Gribonval,et al.  A survey of Sparse Component Analysis for blind source separation: principles, perspectives, and new challenges , 2006, ESANN.

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

[37]  Michael Elad,et al.  Submitted to Ieee Transactions on Image Processing Image Decomposition via the Combination of Sparse Representations and a Variational Approach , 2022 .

[38]  Hongyan Zhang HYPERSPECTRAL IMAGE DENOISING WITH CUBIC TOTAL VARIATION MODEL , 2012 .

[39]  R. Tibshirani,et al.  Sparse Principal Component Analysis , 2006 .

[40]  P. Switzer,et al.  A transformation for ordering multispectral data in terms of image quality with implications for noise removal , 1988 .

[41]  John P. Kerekes,et al.  Hyperspectral Imaging System Modeling , 2003 .

[42]  Jon Atli Benediktsson,et al.  Automatic Generation of Standard Deviation Attribute Profiles for Spectral–Spatial Classification of Remote Sensing Data , 2013, IEEE Geoscience and Remote Sensing Letters.