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Start Over Author "Escande, Paul" Topic inverse problems
5 results on '"Escande, Paul"'

1. Fast wavelet decomposition of linear operators through product-convolution expansions.

Author

Escande, Paul and Weiss, Pierre

Subjects
INVERSE problems, INTEGRAL operators, WAVES (Fluid mechanics), IMPULSE response, WORK design
Abstract

Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately, computing the decomposition is itself a hard problem which is oftentimes out of reach for large-scale problems. The objective of this work is to design fast decomposition algorithms based on another representation called product-convolution expansion. This decomposition can be evaluated efficiently, assuming that a few impulse responses of the operator are available, but it is usually less efficient than the wavelet decomposition when incorporated in iterative methods. The proposed decomposition algorithms, run in quasi-linear time and we provide some numerical experiments to assess its performance for an imaging problem involving space-varying blurs. [ABSTRACT FROM AUTHOR]

Published
2022
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2. Accelerating ℓ 1 − ℓ 2 deblurring using wavelet expansions of operators

Author

Escande, Paul, Weiss, Pierre, Département d'Ingénierie des Systèmes Complexes (DISC), Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), PRIMO (ITAV), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut des Technologies Avancées en sciences du Vivant (ITAV), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Regenerative Medicine and Skeleton research lab (RMeS), Ecole Nationale Vétérinaire, Agroalimentaire et de l'alimentation Nantes-Atlantique (ONIRIS)-Centre hospitalier universitaire de Nantes (CHU Nantes)-Université de Nantes - UFR de Médecine et des Techniques Médicales (UFR MEDECINE), and Université de Nantes (UN)-Université de Nantes (UN)-Institut National de la Santé et de la Recherche Médicale (INSERM)

Subjects
preconditioning, inverse problems, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], image de- blurring, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, GPU programming, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], sparse wavelet expansion, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; Image deblurring is a fundamental problem in imaging, usually solved with compu-tationally intensive optimization procedures. The goal of this paper is to provide new efficient strategies to reduce computing times for simple 1 − 2 deblurring models. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: i) a sparse approximation of the blur operator in wavelet bases, ii) a diagonal preconditioner and iii) an implementation on massively parallel architectures. Combing the three ingredients leads to acceleration factors ranging from 30 to 250 on a typical workstation. For instance, a 1024 × 1024 image can be deblurred in 0.15 seconds.

Published
2018

3. Accelerating l1-l2 deblurring using wavelet expansions of operators

Author

Escande, Paul, Weiss, Pierre, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE), Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), and Université Toulouse 1 Capitole - UT1 (FRANCE)

Subjects
Inverse problems, Autre, Computer Science::Computer Vision and Pattern Recognition, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Preconditioning, Image deblurring, GPU programming, Sparse wavelet expansion
Abstract

Image deblurring is a fundamental problem in imaging, usually solved with computationally intensive optimization procedures. The goal of this paper is to provide new efficient strategies to reduce computing times for simple deblurring models regularized using orthogonal wavelet transforms. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: (i) a sparse approximation of the blur operator in wavelet bases, (ii) a diagonal preconditioner and (iii) an implementation on massively parallel architectures. Combining the three ingredients leads to acceleration factors ranging from 4 to 250 on a typical workstation. For instance, a 1024 1024 image can be deblurred in 0.15 s.

Published
2018

4. Real-time $\ell^1$ − $\ell^2$ deblurring using wavelet expansions of operators

Author

Escande, Paul, Weiss, Pierre, Département de Mathématiques, Informatique, Automatique (DMIA), Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut des Technologies Avancées en sciences du Vivant (ITAV), Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
inverse problems, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Numerical Analysis (math.NA), GPU programming, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Optimization and Control (math.OC), preconditioning, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], FOS: Mathematics, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Mathematics - Numerical Analysis, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, sparse wavelet expansion, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], image de-blurring
Abstract

Image deblurring is a fundamental problem in imaging, usually solved with com-putationally intensive optimization procedures. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: i) a sparse approximation of the blur operator in wavelet bases, ii) a diagonal preconditioner and iii) an implementation on massively parallel architectures. Combing the three ingredients leads to acceleration factors ranging from 30 to 250 on a typical workstation. For instance, a 1024 x 1024 image can be deblurred in 0.15 seconds, which corresponds to real-time.

Published
2015

5. Accelerating [formula omitted] deblurring using wavelet expansions of operators.

Author

Escande, Paul and Weiss, Pierre

Subjects
*WAVELET transforms, *PROBLEM solving, *ORTHOGONAL functions, *MATHEMATICAL optimization, *SPARSE approximations
Abstract

Image deblurring is a fundamental problem in imaging, usually solved with computationally intensive optimization procedures. The goal of this paper is to provide new efficient strategies to reduce computing times for simple deblurring models regularized using orthogonal wavelet transforms. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: (i) a sparse approximation of the blur operator in wavelet bases, (ii) a diagonal preconditioner and (iii) an implementation on massively parallel architectures. Combining the three ingredients leads to acceleration factors ranging from 4 to 250 on a typical workstation. For instance, a 1024 × 1024 image can be deblurred in 0.15 s. [ABSTRACT FROM AUTHOR]

Published
2018
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