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Hyperspectral Image Super-Resolution via Deep Prior regularization With parameter estimation

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 2022年第4期32卷 1708-1723页

作者： Wang, Xiuheng Chen, Jie Wei, Qi Richard, Cedric Northwestern Polytech Univ Sch Marine Sci & Technol Xian 710072 Peoples R China JP Morgan New York NY 10017 USA Univ Cote dAzur OCA CNRS F-06108 Nice France

Hyperspectral image (HSI) super-resolution is commonly used to overcome the hardware limitations of existing hyperspectral imaging systems on spatial resolution. It fuses a low-resolution (LR) HSI and a high-resolution (HR) conventional image of the same scene to obtain an HR HSI. In this work, we propose a method that integrates a physical model and deep prior information. Specifically, a novel, yet effective two-stream fusion network is designed to serve as a regularizer for the fusion problem. This fusion problem is formulated as an optimization problem whose solution can be obtained by solving a Sylvester equation. Furthermore, the regularization parameter is simultaneously estimated to automatically adjust contribution of the physical model and the learned prior to reconstruct the final HR HSI. Experimental results on both simulated and real data demonstrate the superiority of the proposed method over other state-of-the-art methods on both quantitative and qualitative comparisons.

关键词： Superresolution Hyperspectral imaging Optimization Tensors Spatial resolution Degradation Matrix decomposition HSI super-resolution deep learning fusion Sylvester equation regularization parameter estimation

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regularization parameter estimation for Non-Negative Hyperspectral Image Deconvolution

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2016年第11期25卷 5316-5330页

作者： Song, Yingying Brie, David Djermoune, El-Hadi Henrot, Simon Univ Lorraine Ctr Rech Automat Nancy F-54506 Vandoeuvre Les Nancy France Univ Lorraine Ctr Natl Rech Sci F-54506 Vandoeuvre Les Nancy France Signal & Image Dept Grenoble Images Parole Signal Automat Lab F-38402 St Martin Dheres France

This paper aims at studying a method to automatically estimate the regularization parameters of non-negative hyperspectral image deconvolution methods. The deconvolution problem is formulated as a multi-objective optimization problem and the properties of the corresponding response surface are studied. Based on these properties, the minimum distance criterion (MDC) and the maximum curvature criterion (MCC) are proposed to estimate regularization parameters especially for the non-negativity constrained deconvolution problem. MDC has good theoretical properties (convexity and uniqueness) but requires to choose a reference point. On the contrary, MCC does not need to choose any reference point but does not have interesting theoretical properties. A grid-search-based approach to minimize the computational cost of MDC and MCC is proposed. It results in fast approaches to estimate the regularization parameters. Based on simulated 2D images, the proposed approaches are compared with the state-of-the-art methods, confirming the effectiveness of the MDC and MCC for the non-negativity constrained image deconvolution problem. In the case of non-negative hyperpsectral image deconvolution, the fast MDC yields better performances than the fast MCC. An application to real-world hyperspectral fluorescence microscopy images is also provided;it confirms the superiority of MDC.

关键词： Non-negative hyperspectral image deconvolution multi-objective optimization regularization parameter estimation

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Blind separation of structural modes by compact-bandwidth regularization

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2019年 131卷 288-316页

作者： Wang, Li Huang, Min Lu, Zhong-Rong Sun Yat Sen Univ Sch Aeronaut & Astronaut Guangzhou Guangdong Peoples R China Sun Yat Sen Univ Sch Intelligent Syst Engn Guangzhou Guangdong Peoples R China

Operational modal analysis (OMA) has received tremendous interest from engineering fields in recent years. This paper develops a compact-bandwidth regularization approach for OMA within the signal processing framework. The key ingredient lies in the fact that a structural mode is always compact in the frequency domain and this results in the compact-bandwidth constraint for structural modes. To implicitly enforce the compact-bandwidth constraint, the compact-bandwidth regularization is introduced to conventional blind modal separation. Then, the alternating minimization algorithm is used to iteratively get the solution in the immediately-at-once or one-by-one manner. In proceeding so, the spectrum-peak-based rule is adopted for choice of initial modal parameters and the L-curve method in conjunction with a theoretically derived bound is applied to estimate a proper regularization parameter. Numerical examples and an experimental test case are studied along with comparison to some usual OMA approaches to see the performance and advantages of the proposed approach in modal identification. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Compact-bandwidth regularization Operational modal analysis Alternating minimization algorithm regularization parameter estimation Closely spaced modes

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Efficient estimation of regularization parameters via downsampling and the singular value expansion

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BIT NUMERICAL MATHEMATICS 2017年第2期57卷 499-529页

作者： Renaut, Rosemary A. Horst, Michael Wang, Yang Cochran, Douglas Hansen, Jakob Arizona State Univ Sch Math & Stat Sci POB 871804 Tempe AZ 85287 USA Ohio State Univ Dept Math 100 Math Tower231 West 18th Ave Columbus OH 43210 USA Hong Kong Univ Sci & Technol Dept Math Kowloon Hong Kong Peoples R China Arizona State Univ Sch Elect Comp & Energy Engn Ira A Fulton Sch Engn POB 875706 Tempe AZ 85287 USA Univ Penn David Rittenhouse Lab 209 S 33rd St Philadelphia PA 19104 USA

The solution, , of the linear system of equations arising from the discretization of an ill-posed integral equation with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution approximating the Galerkin coefficients of f(t) is found as the minimizer of , where is given by the Galerkin coefficients of g(s). depends on the regularization parameter that trades off between the data fidelity and the smoothing norm determined by L, here assumed to be diagonal and invertible. The Galerkin method provides the relationship between the singular value expansion of the continuous kernel and the singular value decomposition of the discrete system matrix for square integrable kernels. We prove that the kernel maintains square integrability under left and right multiplication by bounded functions and thus the relationship also extends to appropriately weighted kernels. The resulting approximation of the integral equation permits examination of the properties of the regularized solution independent of the sample size of the data. We prove that consistently down sampling both the system matrix and the data provides a small scale system that preserves the dominant terms of the right singular subspace of the system and can then be used to estimate the regularization parameter for the original system. When g(s) is directly measured via its Galerkin coefficients the regularization parameter is preserved across resolutions. For measurements of g(s) a scaling argument is required to move across resolutions of the systems when the regularization parameter is found using a regularization parameter estimation technique that depends on the knowledge of the variance in the data. Numerical results illustrate the theory and demonstrate the practicality of the approach for regularization parameter estimation using generalized cross validation, unbiased predictive risk estimation and the discrepancy principle applied to both the system of equations, and to the regulari

关键词： Singular value expansion Singular value decomposition Ill-posed inverse problem Tikhonov regularization regularization parameter estimation

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Spatial resolution improvement of hyperspectral images by deconvolution and joint unmixing-deconvolution

Spatial resolution improvement of hyperspectral images by de...

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作者： Yingying Song Universite de Lorraine

学位级别：博士

A hyperspectral image is a 3D data cube in which every pixel provides local spectral information about a scene of interest across a large number of contiguous bands. The observed images may suﬀer from degradation due to the measuring device, resulting in a convolution or blurring of the images. Hyperspectral image deconvolution (HID) consists in removing the blurring to improve the spatial resolution of images at best. A Tikhonov-like HID criterion with non-negativity constraint is consid- ered here. This method considers separable spatial and spectral regularization terms whose strength are controlled by two regularization parameters. First part of this thesis proposes the maximum curvature criterion (MCC) and the minimum distance criterion (MDC) to automatically estimate these regularization parameters by formulating the deconvolution problem as a multi-objective opti- mization problem. The second part of this thesis proposes the sliding block regularized (SBR-LMS) algorithm for the online deconvolution of hypserspectral images as provided by whiskbroom and pushbroom scanning systems. The proposed algorithm accounts for the convolution kernel non- causality and including non-quadratic regularization terms while maintaining a linear complexity compatible with real-time processing in industrial applications. The third part of this thesis pro- poses joint unmixing-deconvolution methods based on the Tikhonov criterion in both oﬄine and online contexts. The non-negativity constraint is added to improve their performances.

关键词： non-negative hyperspectral image deconvolution multi-objective optimization regularization parameter estimation online deconvolution zero-attracting LMS joint unmixing and deconvolution

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HYBRID AND ITERATIVELY REWEIGHTED regularization BY UNBIASED PREDICTIVE RISK AND WEIGHTED GCV FOR PROJECTED SYSTEMS

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2017年第2期39卷 B221-B243页

作者： Renaut, Rosemary A. Vatankhah, Saeed Ardestani, Vahid E. Arizona State Univ Sch Math & Stat Sci Tempe AZ 85287 USA Univ Tehran Inst Geophys Tehran Iran

Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace approximation to the full problem. Determination of the regularization, parameter for the projected problem by unbiased predictive risk estimation, generalized cross validation, and discrepancy principle techniques is investigated. It is shown that the regularized parameter obtained by the unbiased predictive risk estimator can provide a good estimate which can be used for a full problem that is moderately to severely ill-posed. A similar analysis provides the weight parameter for the weighted generalized cross validation such that the approach is also useful in these cases, and also explains why the generalized cross validation without weighting is not always useful. All results are independent of whether systems are over or underdetermined. Numerical simulations for standard one-dimensional test problems and two-dimensional data, for both image restoration and tomographic image reconstruction, support the analysis and validate the techniques. The size of the projected problem is found using an extension of a noise revealing function for the projected problem [I. Hnetynkova, M. Plesinger, and Z. Strakos, BIT Numer. Math., 49 (2009), pp. 669-696]. Furthermore, an iteratively reweighted regularization approach for edge preserving regularization is extended for projected systems, providing stabilization of the solutions of the projected systems and reducing dependence on the determination of the size of the projected subspace.

关键词： large-scale inverse problems Golub Kahan bidiagonalization regularization parameter estimation unbiased predictive risk estimator discrepancy principle generalized cross validation iteratively reweighted schemes

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A New Method of regularization parameter estimation for Source Localization

A New Method of Regularization Parameter Estimation for Sour...

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2011 IEEE CIE International Conference on Radar(2011年IEEE国际雷达会议RADAR 2011)

作者： Juanru Huang Mei Dong Shili Li National Key Lab for Radar Signal Processing Xidian Univ. Xi’an 710071 China

ISBN: (纸本)9781424484447

The problem of estimating the regularization parameter for source localization in sparse-regularization framework is considered in this paper. We employ the distribution about every entry of the square of the Frobenius norm of noise to obtain a larger and more appropriate regularization parameter. The paper analyzes the reason that we can not simply set it equal to the square of the Frobenius norm of noise and presents the estimation in two practical cases: one works without taking singular value decomposition (SVD) of sensor outputs;the other works after that pretreatment for large data quantity. The simulation results demonstrate that the proposed method has many advantages, including enhancing resolution, effectively suppressing spurious peaks, improving robustness to noise, as well as increasing the number of resolvable sources.

关键词： sparse representation regularization parameter estimation source localization sensor array processing

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MINIMUM DISTANCE CRITERION FOR NON-NEGATIVE HYPERSPECTRAL IMAGE DECONVOLUTION 41

MINIMUM DISTANCE CRITERION FOR NON-NEGATIVE HYPERSPECTRAL IM...

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Song, Yingying Brie, David Djermoune, El-Hadi Henrot, Simon Univ Lorraine Ctr Rech Automat Nancy CNRS Blvd Aiguilletes BP 239 F-54506 Vandoeuvre Les Nancy France

ISBN: (纸本)9781479999880

This work aims at studying a method to automatically estimate regularization parameters of hyperspectral images deconvolution methods. The deconvolution problem is formulated as a multi-objective optimization problem and the properties of the corresponding response surface are studied. Based on these properties, the minimum distance criterion (MDC) is proposed to estimate regularization parameters. It has good theoretical properties (uniqueness, robustness) from which a grid search based approach is proposed. It results in a fast approach to estimate the regularization parameters.

关键词： Hyperspectral image deconvolution multi-objective optimization regularization parameter estimation

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Numerical Methods for parameter estimation in Poisson Data Inversion

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2015年第3期52卷 397-413页

作者： Zanni, Luca Benfenati, Alessandro Bertero, Mario Ruggiero, Valeria Univ Modena & Reggio Emilia Dipartimento Sci Fis Informat & Matemat I-41125 Modena Italy Univ Ferrara Dipartimento Matemat & Informat I-44122 Ferrara Italy Univ Genoa Dipartimento Informat Bioingn Robot & Ingn Sistem I-16146 Genoa Italy

In a regularized approach to Poisson data inversion, the problem is reduced to the minimization of an objective function which consists of two terms: a data-fidelity function, related to a generalized Kullback-Leibler divergence, and a regularization function expressing a priori information on the unknown image. This second function is multiplied by a parameter , sometimes called regularization parameter, which must be suitably estimated for obtaining a sensible solution. In order to estimate this parameter, a discrepancy principle has been recently proposed, that implies the minimization of the objective function for several values of . Since this approach can be computationally expensive, it has also been proposed to replace it with a constrained minimization, the constraint being derived from the discrepancy principle. In this paper we intend to compare the two approaches from the computational point of view. In particular, we propose a secant-based method for solving the discrepancy equation arising in the first approach;when this root-finding algorithm can be combined with an efficient solver of the inner minimization problems, the first approach can be competitive and sometimes faster than the second one.

关键词： Poisson noise regularization parameter estimation Discrepancy principle Hypersurface regularization Seminorm regularization

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MINIMUM DISTANCE CRITERION FOR NON-NEGATIVE HYPERSPECTRAL IMAGE DECONVOLUTION

MINIMUM DISTANCE CRITERION FOR NON-NEGATIVE HYPERSPECTRAL IM...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Yingying Song David Brie El-Hadi Djermoune Simon Henrot Université de Lorraine Centre de Recherche en Automatique de Nancy (CRAN) CNRS Boulevard des Aiguilletes B.P. 239 F-54506 Vandoeuvre-lès-Nancy France

ISBN: (纸本)9781479999897

关键词： Hyperspectral image deconvolution multi-objective optimization regularization parameter estimation

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