Bayesian fusion of multispectral and hyperspectral images using a block coordinate descent method

This paper studies a new Bayesian optimization algorithm for fusing hyperspectral and multispectral images. The hyperspectral image is supposed to be obtained by blurring and subsampling a high spatial and high spectral target image. The multispectral image is modeled as a spectral mixing version of the target image. By introducing appropriate priors for parameters and hyperparameters, the fusion problem is formulated within a Bayesian estimation framework, which is very convenient to model the noise and the target image. The high spatial resolution hyperspectral image is then inferred from its posterior distribution. To compute the Bayesian maximum a posteriori estimator associated with this posterior, an alternating direction method of multipliers within block coordinate descent algorithm is proposed. Simulation results demonstrate the efficiency of the proposed fusion method when compared with several state-of-the-art fusion techniques.

[1]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[2]  Jocelyn Chanussot,et al.  Fusion of hyperspectral and panchromatic images using multiresolution analysis and nonlinear PCA band reduction , 2011, 2011 IEEE International Geoscience and Remote Sensing Symposium.

[3]  Yifan Zhang,et al.  Noise-Resistant Wavelet-Based Bayesian Fusion of Multispectral and Hyperspectral Images , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[4]  Jean-Yves Tourneret,et al.  Bayesian fusion of hyperspectral and multispectral images , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[5]  Russell C. Hardie,et al.  MAP estimation for hyperspectral image resolution enhancement using an auxiliary sensor , 2004, IEEE Transactions on Image Processing.

[6]  Naoto Yokoya,et al.  Hyperspectral Pansharpening: A Review , 2015, IEEE Geoscience and Remote Sensing Magazine.

[7]  J. Engels,et al.  Pansharpening of Hyperspectral Images in Urban Areas , 2012 .

[8]  José M. Bioucas-Dias,et al.  An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems , 2009, IEEE Transactions on Image Processing.

[9]  Jean-Yves Tourneret,et al.  Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation , 2015, IEEE Transactions on Image Processing.

[10]  Todd Wittman,et al.  A variational approach to hyperspectral image fusion , 2009, Defense + Commercial Sensing.

[11]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[12]  Jean-Yves Tourneret,et al.  Bayesian Fusion of Multi-Band Images , 2013, IEEE Journal of Selected Topics in Signal Processing.

[13]  Tongxing Lu,et al.  Solution of the matrix equation AX−XB=C , 2005, Computing.

[14]  V. K. Shettigara,et al.  A generalized component substitution technique for spatial enhancement of multispectral images using , 1992 .

[15]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[16]  Antonio J. Plaza,et al.  Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[17]  David J. Fleming.  Effect of relative spectral response on multi-spectral measurements and NDVI from different remote sensing systems , 2006 .

[18]  Nikolas P. Galatsanos,et al.  Stochastic methods for joint registration, restoration, and interpolation of multiple undersampled images , 2006, IEEE Transactions on Image Processing.

[19]  A. Dawid.  Some matrix-variate distribution theory: Notational considerations and a Bayesian application , 1981 .

[20]  Nebiye Musaoglu,et al.  Merging hyperspectral and panchromatic image data: qualitative and quantitative analysis , 2009 .

[21]  José M. Bioucas-Dias,et al.  Fast Image Recovery Using Variable Splitting and Constrained Optimization , 2009, IEEE Transactions on Image Processing.

[22]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[23]  Aggelos K. Katsaggelos,et al.  A survey of classical methods and new trends in pansharpening of multispectral images , 2011, EURASIP J. Adv. Signal Process..

[24]  P. Gustafson,et al.  Conservative prior distributions for variance parameters in hierarchical models , 2006 .

[25]  Peter J. Liu,et al.  Using Gaussian process regression to denoise images and remove artefacts from microarray data , 2007 .

[26]  Jean-Yves Tourneret,et al.  Hyperspectral and Multispectral Image Fusion Based on a Sparse Representation , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[27]  Dimitris G. Manolakis,et al.  Detection algorithms for hyperspectral imaging applications , 2002, IEEE Signal Process. Mag..

[28]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[29]  Guangyi Chen,et al.  Super-Resolution of Hyperspectral Imagery Using Complex Ridgelet Transform , 2012, Int. J. Wavelets Multiresolution Inf. Process..

[30]  J. Zhou,et al.  A wavelet transform method to merge Landsat TM and SPOT panchromatic data , 1998 .