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Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling [article]

Shanshan Wu, Alexandros G. Dimakis, Sujay Sanghavi, Felix X. Yu, Daniel Holtmann-Rice, Dmitry Storcheus, Afshin Rostamizadeh, Sanjiv Kumar
2019 arXiv   pre-print
Our method can be seen as a data-driven way to learn a compressed sensing measurement matrix. We compare the empirical performance of 10 algorithms over 6 sparse datasets (3 synthetic and 3 real).  ...  The convex ℓ_1 decoder prevents gradient propagation as needed in standard gradient-based training.  ...  Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling = % (') = % ' = sign( ' ) − ' − % ' (1) (') BN − % − % % (%4') (%) BN % = sign( % ) … 5 = ReLU( (%4') ) Figure 1.  ... 
arXiv:1806.10175v4 fatcat:rm4kjn7sw5fyxlzulnqtyh6f3y

Dynamic Proximal Unrolling Network for Compressive Imaging [article]

Yixiao Yang, Ran Tao, Kaixuan Wei, Ying Fu
2021 arXiv   pre-print
In this paper, a dynamic proximal unrolling network (dubbed DPUNet) was proposed, which can handle a variety of measurement matrices via one single model without retraining.  ...  Compressive imaging aims to recover a latent image from under-sampled measurements, suffering from a serious ill-posed inverse problem.  ...  Further several CNN-based approaches were developed, which learn the inverse map from compressively sensed measurements to reconstructed images [28, 37, 41] .  ... 
arXiv:2107.11007v2 fatcat:kejgz4xl2zcfvdzbywjhiyriy4

Gradient-Based Learning of Discrete Structured Measurement Operators for Signal Recovery [article]

Jonathan Sauder and Martin Genzel and Peter Jung
2022 arXiv   pre-print
While the potential of gradient-based learning via the unrolling of iterative recovery algorithms has been demonstrated, it has remained unclear how to leverage this technique when the set of admissible  ...  Our approach is formalized by GLODISMO (Gradient-based Learning of DIscrete Structured Measurement Operators).  ...  LISTA has inspired a line of research on unrolled optimization algorithms for compressed sensing.  ... 
arXiv:2202.03391v1 fatcat:lxlipdn6x5ejvbl3xnksbn4t3m

Memory-Efficient Learning for Large-Scale Computational Imaging

Michael Kellman, Kevin Zhang, Eric Markley, Jon Tamir, Emrah Bostan, Michael Lustig, Laura Waller
2020 IEEE Transactions on Computational Imaging  
We demonstrate our method on a compressed sensing example, as well as two largescale real-world systems: 3D multi-channel magnetic resonance imaging and super-resolution optical microscopy.  ...  Termed physics-based networks, they incorporate both the known physics of the system via its forward model, and the power of deep learning via data-driven training.  ...  ACKNOWLEDGMENT The authors would like to thank Ke Wang for his insightful discusses on image reconstruction and deep learning, as well as Professor Ben Recht for our preliminary discussions on this work  ... 
doi:10.1109/tci.2020.3025735 fatcat:rifktsymajconi3sts2t25qzvi

Memory-efficient Learning for Large-scale Computational Imaging [article]

Michael Kellman, Kevin Zhang, Jon Tamir, Emrah Bostan, Michael Lustig, Laura Waller
2020 arXiv   pre-print
We demonstrate our method on a small-scale compressed sensing example, as well as two large-scale real-world systems: multi-channel magnetic resonance imaging and super-resolution optical microscopy.  ...  However, for real-world large-scale inverse problems, computing gradients via backpropagation is infeasible due to memory limitations of graphics processing units.  ...  Learned measurements for compressed sensing Compressed sensing combines random measurements and regularized optimization to reduce the sampling requirements of a signal below the Nyquist rate [19] .  ... 
arXiv:2003.05551v1 fatcat:pm5vkz2pj5es7bkhnwodv4ckhy

Self-Supervised Physics-Based Deep Learning MRI Reconstruction Without Fully-Sampled Data [article]

Burhaneddin Yaman, Seyed Amir Hossein Hosseini, Steen Moeller, Jutta Ellermann, Kâmil Uǧurbil, Mehmet Akçakaya
2019 arXiv   pre-print
Deep learning (DL) has emerged as a tool for improving accelerated MRI reconstruction.  ...  A common strategy among DL methods is the physics-based approach, where a regularized iterative algorithm alternating between data consistency and a regularizer is unrolled for a finite number of iterations  ...  This can be solved via conjugate gradient to avoid matrix inversion [8] .  ... 
arXiv:1910.09116v1 fatcat:ytd6a5pwcbfjlpzcfi3fellwuy

Deep Unrolling for Light Field Compressed Acquisition Using Coded Masks

Guillaume Le Guludec, Christine Guillemot
2022 IEEE Access  
INDEX TERMS Light field imaging, compressed sensing, deep learning, inverse problems, algorithm unrolling.  ...  Compressed sensing using color-coded masks has been recently considered for capturing light fields using a small number of measurements.  ...  CONCLUSION In this paper, we have presented a new deep architecture, based on unrolled optimization with learned priors, for the reconstruction of compressively acquired light fields via color-coded masks  ... 
doi:10.1109/access.2022.3168362 fatcat:wg5gbmutmnbn5h7kbe7to27ufe

JR2net: A Joint Non-Linear Representation and Recovery Network for Compressive Spectral Imaging [article]

Brayan Monroy, Jorge Bacca, Henry Arguello
2022 arXiv   pre-print
These methods use a deep neural network (DNN) as an image generator to learn non-linear mapping from compressed measurements to the spectral image.  ...  Deep learning models are state-of-the-art in compressive spectral imaging (CSI) recovery.  ...  Representation Learning The representation learning consists in learn a non-linear representation 𝜶 ∈ R 𝐻 𝑊 𝐹 from a given spectral image f ∈ R 𝐻 𝑊 𝐶 , via the learning of a decoder 𝑫 (•) which  ... 
arXiv:2205.07770v1 fatcat:sajbzktaz5akjihfrlfxlrq7se

Unrolled Optimization with Deep Priors [article]

Steven Diamond and Vincent Sitzmann and Felix Heide and Gordon Wetzstein
2018 arXiv   pre-print
measurements taken under a known physical image formation model.  ...  We show that instances of the framework outperform the state-of-the-art by a substantial margin for a wide variety of imaging problems, such as denoising, deblurring, and compressed sensing magnetic resonance  ...  Compressed sensing MRI In compressed sensing (CS) MRI, a latent image x is measured in the Fourier domain with subsampling. Following [27] , we assume noise free measurements.  ... 
arXiv:1705.08041v2 fatcat:c44in7dpbzhhnjvzvlao3kpi6m

DNU: Deep Non-Local Unrolling for Computational Spectral Imaging

Lizhi Wang, Chen Sun, Maoqing Zhang, Ying Fu, Hua Huang
2020 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
Our data-driven prior is integrated as a regularizer into the reconstruction problem. Then, we propose to unroll the reconstruction problem into an optimization-inspired deep neural network.  ...  Finally, we learn the complete parameters in the network through end-to-end training, enabling robust performance with high spatial-spectral fidelity.  ...  Interpretable Unrolling-based Reconstruction Given the compressive image g and the sensing matrix Φ, the subsequent task is to estimate the underlying spectral image.  ... 
doi:10.1109/cvpr42600.2020.00173 dblp:conf/cvpr/WangSZF020 fatcat:jhzpiwj2b5fjjd6hotf3gclxga

D^2UF: Deep Coded Aperture Design and Unrolling Algorithm for Compressive Spectral Image Fusion [article]

Roman Jacome, Jorge Bacca, Henry Arguello
2022 arXiv   pre-print
This work presents the fusion of the compressive measurements of a low-spatial high-spectral resolution coded aperture snapshot spectral imager (CASSI) architecture and a high-spatial low-spectral resolution  ...  To overcome this issue, compressive spectral image fusion (CSIF) employs the projected measurements of two CSI architectures with different resolutions to estimate a high-spatial high-spectral resolution  ...  The model can be also expressed a matrix-vector product as g m = Φ m f + n m , (8) where g m ∈ R M N is the compressive measurements, Φ m ∈ R M N ×M N L is the sensing matrix and n m ∈ R M N stands for  ... 
arXiv:2205.12158v1 fatcat:en4jaan4bzc7rdggz7s3ijco5e

Real-time compressed imaging of scattering volumes

Ohad Menashe, Alexander Bronstein
2014 2014 IEEE International Conference on Image Processing (ICIP)  
We also show a simple greedy algorithm for learning the optimal illumination patterns. Our results demonstrate faithful reconstruction from highly compressed measurements.  ...  set of compressed measurements.  ...  procedure for a binary sensing matrix. the measurements E of A.  ... 
doi:10.1109/icip.2014.7025264 dblp:conf/icip/MenasheB14 fatcat:6irbshfggvfcljvlqa5uuozmqe

Designing recurrent neural networks by unfolding an l1-l1 minimization algorithm [article]

Hung Duy Le, Huynh Van Luong, Nikos Deligiannis
2019 arXiv   pre-print
We evaluate the proposed model in the task of reconstructing video frames from compressive measurements and show that it outperforms several state-of-the-art RNN models.  ...  Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem.  ...  For each sequence, we obtain a sequence of measurements x 1:20 using a trainable linear sensing matrix A ∈ R m×n , with n = 256 and m < n.  ... 
arXiv:1902.06522v1 fatcat:vzjc2ylhrbczvcz2jhbkkrgfvq

Deep Unfolding with Normalizing Flow Priors for Inverse Problems [article]

Xinyi Wei, Hans van Gorp, Lizeth Gonzalez Carabarin, Daniel Freedman, Yonina C. Eldar, Ruud J.G. van Sloun
2022 arXiv   pre-print
By combining a-priori knowledge of the forward measurement model with learned (proximal) mappings based on deep networks, these methods yield solutions that are both physically feasible (data-consistent  ...  Many application domains, spanning from computational photography to medical imaging, require recovery of high-fidelity images from noisy, incomplete or partial/compressed measurements.  ...  More specifically, within the framework of compressed sensing, in which signals are to be reconstructed from a set of compressed measurements, deep learning methods have improved both image quality and  ... 
arXiv:2107.02848v2 fatcat:go27sivhubb7lbki2med32wni4

Robust Deep Compressive Sensing with Recurrent-Residual Structural Constraints [article]

Jun Niu
2022 arXiv   pre-print
The adaptive sensing nature further makes it an ideal candidate for color image CS via leveraging channel correlation.  ...  Existing deep compressive sensing (CS) methods either ignore adaptive online optimization or depend on costly iterative optimizer during reconstruction.  ...  DEEP COMPRESSIVE SENSING WITH STRUCTURAL CONSTRAINTS AND ONLINE OPTIMIZATION Compressive sensing aims to efficiently acquire a compressible signal x and then reconstruct the original signal from samplings  ... 
arXiv:2207.07301v1 fatcat:6llqqmwmsjegfoiplzmveeznvy
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