Training Adaptive Reconstruction Networks for Blind Inverse Problems

Alban Gossard; Pierre Weiss

Pré-Publication, Document De Travail Année : 2023

Training Adaptive Reconstruction Networks for Blind Inverse Problems

(1) , (1)

Alban Gossard

Fonction : Auteur
PersonId : 743847
IdHAL : albangossard
ORCID : 0000-0001-6782-5080

Institut de Mathématiques de Toulouse UMR5219

Pierre Weiss

Fonction : Auteur
PersonId : 3546
IdHAL : pierre-weiss
ORCID : 0000-0001-9083-214X
IdRef : 129563196

Institut de Mathématiques de Toulouse UMR5219

Résumé

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these networks suffer from a major defect: when trained on a given forward operator, they do not generalize well to a different one. The aim of this paper is twofold. First, we show through various applications that training the network with a family of forward operators allows solving the adaptivity problem without compromising the reconstruction quality significantly. Second, we illustrate that this training procedure allows tackling challenging blind inverse problems. Our experiments include partial Fourier sampling problems arising in magnetic resonance imaging (MRI) with sensitivity estimation and off-resonance effects, computerized tomography (CT) with a tilted geometry and image deblurring with Fresnel diffraction kernels.

Mots clés

Blind inverse problems Self-calibration Adaptivity Model-based reconstruction Convolutional neural network Unrolled networks MRI reconstruction Computerized tomography Blind deblurring

Domaines

Traitement du signal et de l'image [eess.SP] Apprentissage [cs.LG] Optimisation et contrôle [math.OC]

Fichier principal

Training_Adaptive_Reconstruction_Networks_for_Blind_Inverse_Problems.pdf (4.42 Mo)

BLUR_tab_scores-crop.pdf (15.21 Ko)

CT_tab_scores1c-crop.pdf (14.35 Ko)

CT_tab_scores2c-crop.pdf (15.05 Ko)

f.png (49.19 Ko)

f_Nlines=16_idimg=20.png (57.48 Ko)

f_tilde0_Nlines=16_idimg=20_PP.png (73.66 Ko)

f_tilde0_Nlines=16_idimg=20_family.png (58.69 Ko)

f_tilde0_Nlines=16_idimg=20_fixed.png (59.24 Ko)

f_tilde0_coco_idimg=10_seed=7_noiselevel=0.0001_fixed.png (212.87 Ko)

f_tilde_Nlines=16_idimg=20_PP.png (42.46 Ko)

f_tilde_Nlines=16_idimg=20_family.png (57.62 Ko)

f_tilde_Nlines=16_idimg=20_fixed.png (50.81 Ko)

f_tilde_Nlines=16_idimg=20_nonblind_PP.png (40.37 Ko)

f_tilde_Nlines=16_idimg=20_nonblind_family.png (57.87 Ko)

f_tilde_Nlines=16_idimg=20_nonblind_fixed.png (50.8 Ko)

f_tilde_Nlines=16_idimg=20_theta0_fixed.png (57.51 Ko)

f_tilde_coco_idimg=10_seed=7_noiselevel=0.0001_fixed.png (209.05 Ko)

f_tilde_coco_idimg=10_seed=7_noiselevel=0.0001_nonblind_fixed.png (212.66 Ko)

f_tilde_coco_idimg=10_seed=7_noiselevel=0.0001_theta0_fixed.png (188.44 Ko)

f_tilde_family.png (48.38 Ko)

f_tilde_otherxi.png (52.73 Ko)

f_tilde_pseudoinv_Nlines=16_idimg=20_theta0_fixed.png (60.02 Ko)

f_tilde_truexi.png (49.29 Ko)

fig1c_b_35.39.png (27.79 Ko)

fig1c_c_32.89.png (29.58 Ko)

fig1c_d_25.70.png (30.19 Ko)

fig1c_inv27.87.png (33.36 Ko)

fig6_16_04_1.341_1.95.pdf (2.13 Ko)

fig6_17_04_1.341_1.95.pdf (2.13 Ko)

fig6_17_14_2.033_0.88.pdf (2.14 Ko)

fig6_17_34_2.100_1.03.pdf (2.16 Ko)

fig6_17_66_0.110_0.13.pdf (2.12 Ko)

fig6_8_00.png (27.8 Ko)

fig6_8_11_36.62.png (28.19 Ko)

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fig6_8_22_29.68.png (24.42 Ko)

fig6_8_23_37.21.png (22.22 Ko)

fig6_8_31_39.53.png (22.38 Ko)

fig6_8_32_29.68.png (24.43 Ko)

fig6_8_33_33.48.png (22.19 Ko)

fig7_2_hest_9.03.png (150 B)

fig7_2_trueh.png (281 B)

fig7_2_truex.png (39.86 Ko)

fig7_2_xest_20.61.png (30.11 Ko)

fig7_2_xideal_28.12.png (32.11 Ko)

fig7_2_y_19.64.png (30.95 Ko)

fig7_5_hest_19.02.png (150 B)

fig7_5_trueh.png (216 B)

fig7_5_truex.png (41.16 Ko)

fig7_5_xest_29.11.png (28.33 Ko)

fig7_5_xideal_32.31.png (29.7 Ko)

fig7_5_y_27.26.png (31.27 Ko)

fig7_6_hest_26.93.png (175 B)

fig7_6_trueh.png (212 B)

fig7_6_truex.png (31.01 Ko)

fig7_6_xest_30.72.png (25.79 Ko)

fig7_6_xideal_35.00.png (24.75 Ko)

fig7_6_y_25.41.png (31.7 Ko)

fig7_7_hest_9.16.png (162 B)

fig7_7_trueh.png (269 B)

fig7_7_truex.png (23.42 Ko)

fig7_7_xest_19.40.png (27.35 Ko)

fig7_7_xideal_25.69.png (25.59 Ko)

fig7_7_y_18.11.png (31.74 Ko)

fig7_8_hest_26.20.png (150 B)

fig7_8_trueh.png (203 B)

fig7_8_truex.png (32.96 Ko)

fig7_8_xest_35.83.png (20.42 Ko)

fig7_8_xideal_37.29.png (17.63 Ko)

fig7_8_y_31.55.png (28.74 Ko)

hmeasure_coco_idimg=10_seed=7_noiselevel=0.0001.png (669 B)

htrained.png (677 B)

kspace_Nlines=16_idimg=20.png (61.08 Ko)

kspace_center_Nlines=16_idimg=20.pdf (98.53 Ko)

kspace_center_Nlines=16_idimg=20_PP.pdf (97.72 Ko)

kspace_center_Nlines=16_idimg=20_family.pdf (98.81 Ko)

kspace_center_Nlines=16_idimg=20_fixed.pdf (98.15 Ko)

kspace_center_Nlines=16_idimg=20_theta0_fixed.pdf (98.07 Ko)

pi_0.png (42.09 Ko)

pi_2.png (24.46 Ko)

pi_cross_axes.png (43.6 Ko)

pi_cross_diag.png (39.61 Ko)

pi_hor_sf=0.25.png (21 Ko)

pi_vert_sf=0.25.png (48.26 Ko)

piref.png (37.82 Ko)

psf_00.png (411 B)

psf_01.png (751 B)

psf_02.png (503 B)

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psf_04.png (585 B)

psf_05.png (527 B)

psf_06.png (493 B)

tab_fixed_admm_blur-crop.pdf (20.57 Ko)

tab_fixed_admm_drunet-crop.pdf (13.55 Ko)

tab_fixed_den_drunet-crop.pdf (13.66 Ko)

tab_scores_drunet-crop.pdf (15.95 Ko)

xi_0.png (31.78 Ko)

xi_2.png (31.03 Ko)

xiaxes.png (33.92 Ko)

xicons_0.png (31.51 Ko)

xicons_1.png (31.84 Ko)

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xicons_6.png (32.06 Ko)

xidiag.png (34.38 Ko)

xihor.png (29.22 Ko)

xiref.png (34.5 Ko)

xivert.png (32.58 Ko)

y_coco_idimg=10_seed=7_noiselevel=0.0001_theta0_fixed.png (118.04 Ko)

Origine	Fichiers produits par l'(les) auteur(s)

Alban Gossard : Connectez-vous pour contacter le contributeur

https://hal.science/hal-03585120

Soumis le : vendredi 13 octobre 2023-10:15:39

Dernière modification le : mercredi 20 décembre 2023-03:38:45

Dates et versions

hal-03585120 , version 1 (22-02-2022)

hal-03585120 , version 2 (25-02-2022)

hal-03585120 , version 3 (13-11-2022)

hal-03585120 , version 4 (13-10-2023)

hal-03585120 , version 5 (13-12-2023)

Identifiants

HAL Id : hal-03585120 , version 4
ARXIV : 2202.11342

Citer

Alban Gossard, Pierre Weiss. Training Adaptive Reconstruction Networks for Blind Inverse Problems. 2023. ⟨hal-03585120v4⟩

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Training Adaptive Reconstruction Networks for Blind Inverse Problems

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