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  1. Book ; Online: RED-PSM

    Iskender, Berk / Klasky, Marc L. / Bresler, Yoram

    Regularization by Denoising of Partially Separable Models for Dynamic Imaging

    2023  

    Abstract: Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a ... ...

    Abstract Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to efficiently introduce a low-rank prior for the spatio-temporal object. The second is the recent \textit{Regularization by Denoising (RED)}, which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and a computationally efficient and scalable optimization scheme with variable splitting and ADMM. Theoretical analysis proves the convergence of our objective to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method known as TD-DIP. Although the main focus is on dynamic tomography, we also show performance advantages of RED-PSM in a cardiac dynamic MRI setting.
    Keywords Electrical Engineering and Systems Science - Image and Video Processing ; Computer Science - Computer Vision and Pattern Recognition ; Computer Science - Machine Learning
    Subject code 006
    Publishing date 2023-04-07
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Book ; Online: Scatter Correction in X-ray CT by Physics-Inspired Deep Learning

    Iskender, Berk / Bresler, Yoram

    2021  

    Abstract: Scatter due to interaction of photons with the imaged object is a fundamental problem in X-ray Computed Tomography (CT). It manifests as various artifacts in the reconstruction, making its abatement or correction critical for image quality. Despite ... ...

    Abstract Scatter due to interaction of photons with the imaged object is a fundamental problem in X-ray Computed Tomography (CT). It manifests as various artifacts in the reconstruction, making its abatement or correction critical for image quality. Despite success in specific settings, hardware-based methods require modification in the hardware, or increase in the scan time or dose. This accounts for the great interest in software-based methods, including Monte-Carlo based scatter estimation, analytical-numerical, and kernel-based methods, with data-driven learning-based approaches demonstrated recently. In this work, two novel physics-inspired deep-learning-based methods, PhILSCAT and OV-PhILSCAT, are proposed. The methods estimate and correct for the scatter in the acquired projection measurements. Different from previous works, they incorporate both an initial reconstruction of the object of interest and the scatter-corrupted measurements related to it, and use a deep neural network architecture and cost function, both specifically tailored to the problem. Numerical experiments with data generated by Monte-Carlo simulations of the imaging of phantoms reveal consistent improvement over a recent purely projection-domain deep neural network scatter correction method.
    Keywords Physics - Medical Physics ; Computer Science - Machine Learning ; Electrical Engineering and Systems Science - Image and Video Processing
    Subject code 006
    Publishing date 2021-03-21
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Book ; Online: Learning to Bound

    Habi, Hai Victor / Messer, Hagit / Bresler, Yoram

    A Generative Cram\'er-Rao Bound

    2022  

    Abstract: The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the likelihood of the ... ...

    Abstract The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the likelihood of the measurements given the parameters, or equivalently a precise and explicit statistical model for the data. In many applications, such a model is not available. Instead, this work introduces a novel approach to approximate the CRB using data-driven methods, which removes the requirement for an analytical statistical model. This approach is based on the recent success of deep generative models in modeling complex, high-dimensional distributions. Using a learned normalizing flow model, we model the distribution of the measurements and obtain an approximation of the CRB, which we call Generative Cram\'er-Rao Bound (GCRB). Numerical experiments on simple problems validate this approach, and experiments on two image processing tasks of image denoising and edge detection with a learned camera noise model demonstrate its power and benefits.
    Keywords Computer Science - Machine Learning ; Electrical Engineering and Systems Science - Signal Processing
    Publishing date 2022-03-07
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: Dynamic Tomography Reconstruction by Projection-Domain Separable Modeling

    Iskender, Berk / Klasky, Marc L. / Bresler, Yoram

    2022  

    Abstract: In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant. Instead, the ... ...

    Abstract In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant. Instead, the objective is to reconstruct a spatio-temporal representation of the object, which can be displayed as a movie. We analyze conditions for unique and stable solution of this ill-posed inverse problem, and present a recovery algorithm, validating it experimentally. We compare our approach to one based on the recently proposed GMLR variation on deep prior for video, demonstrating the advantages of the proposed approach.
    Keywords Electrical Engineering and Systems Science - Image and Video Processing ; Electrical Engineering and Systems Science - Signal Processing
    Publishing date 2022-04-21
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Article ; Online: Image Recovery via Transform Learning and Low-Rank Modeling: The Power of Complementary Regularizers.

    Wen, Bihan / Li, Yanjun / Bresler, Yoram

    IEEE transactions on image processing : a publication of the IEEE Signal Processing Society

    2020  

    Abstract: Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image/video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches ...

    Abstract Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image/video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properties, we develop an image restoration framework using a transform learning scheme with joint low-rank regularization. The approach owes some of its computational efficiency and good performance to the use of transform learning for adaptive sparse representation rather than the popular synthesis dictionary learning algorithms, which involve approximation of NP-hard sparse coding and expensive learning steps. We demonstrate the proposed framework in various applications to image denoising, inpainting, and compressed sensing based magnetic resonance imaging. Results show promising performance compared to state-of-the-art competing methods.
    Language English
    Publishing date 2020-03-19
    Publishing country United States
    Document type Journal Article
    ISSN 1941-0042
    ISSN (online) 1941-0042
    DOI 10.1109/TIP.2020.2980753
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  6. Book ; Online: Joint Dimensionality Reduction for Separable Embedding Estimation

    Li, Yanjun / Wen, Bihan / Cheng, Hao / Bresler, Yoram

    2021  

    Abstract: Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method that learns ... ...

    Abstract Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method that learns linear embeddings jointly for two feature vectors representing data of different modalities or data from distinct types of entities. We also propose an efficient feature selection method that complements, and can be applied prior to, our joint dimensionality reduction method. Assuming that there exist true linear embeddings for these features, our analysis of the error in the learned linear embeddings provides theoretical guarantees that the dimensionality reduction method accurately estimates the true embeddings when certain technical conditions are satisfied and the number of samples is sufficiently large. The derived sample complexity results are echoed by numerical experiments. We apply the proposed dimensionality reduction method to gene-disease association, and predict unknown associations using kernel regression on the dimension-reduced feature vectors. Our approach compares favorably against other dimensionality reduction methods, and against a state-of-the-art method of bilinear regression for predicting gene-disease associations.
    Keywords Computer Science - Machine Learning
    Subject code 518
    Publishing date 2021-01-14
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  7. Article ; Online: VIDOSAT: High-Dimensional Sparsifying Transform Learning for Online Video Denoising.

    Wen, Bihan / Ravishankar, Saiprasad / Bresler, Yoram

    IEEE transactions on image processing : a publication of the IEEE Signal Processing Society

    2018  Volume 28, Issue 4, Page(s) 1691–1704

    Abstract: Techniques exploiting the sparsity of images in a transform domain are effective for various applications in image and video processing. In particular, transform learning methods involve cheap computations and have been demonstrated to perform well in ... ...

    Abstract Techniques exploiting the sparsity of images in a transform domain are effective for various applications in image and video processing. In particular, transform learning methods involve cheap computations and have been demonstrated to perform well in applications, such as image denoising and medical image reconstruction. Recently, we proposed methods for online learning of sparsifying transforms from streaming signals, which enjoy good convergence guarantees and involve lower computational costs than online synthesis dictionary learning. In this paper, we apply online transform learning to video denoising. We present a novel framework for online video denoising based on high-dimensional sparsifying transform learning for spatio-temporal patches. The patches are constructed either from corresponding 2D patches in successive frames or using an online block matching technique. The proposed online video denoising requires little memory and offers efficient processing. Numerical experiments evaluate the performance of the proposed video denoising algorithms on multiple video data sets. The proposed methods outperform several related and recent techniques, including denoising with 3D DCT, prior schemes based on dictionary learning, non-local means, background separation, and deep learning, as well as the popular VBM3D and VBM4D.
    Language English
    Publishing date 2018-08-16
    Publishing country United States
    Document type Journal Article
    ISSN 1941-0042
    ISSN (online) 1941-0042
    DOI 10.1109/TIP.2018.2865684
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  8. Book ; Online: Learning Filter Bank Sparsifying Transforms

    Pfister, Luke / Bresler, Yoram

    2018  

    Abstract: Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data, and data- ... ...

    Abstract Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data, and data-adaptive sparsifying transforms have demonstrated excellent performance in signal restoration tasks. Sparsifying transforms are typically learned using small sub-regions of data called patches, but these algorithms often ignore redundant information shared between neighboring patches. We show that many existing transform and analysis sparse representations can be viewed as filter banks, thus linking the local properties of patch-based model to the global properties of a convolutional model. We propose a new transform learning framework where the sparsifying transform is an undecimated perfect reconstruction filter bank. Unlike previous transform learning algorithms, the filter length can be chosen independently of the number of filter bank channels. Numerical results indicate filter bank sparsifying transforms outperform existing patch-based transform learning for image denoising while benefiting from additional flexibility in the design process.
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning ; Electrical Engineering and Systems Science - Signal Processing
    Subject code 006
    Publishing date 2018-03-05
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Book ; Online: Improving Robustness of Deep-Learning-Based Image Reconstruction

    Raj, Ankit / Bresler, Yoram / Li, Bo

    2020  

    Abstract: Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem solvers has ... ...

    Abstract Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem solvers has generated much excitement for medical imaging including CT and MRI, but recently a similar vulnerability has also been demonstrated for these tasks. We show that for such inverse problem solvers, one should analyze and study the effect of adversaries in the measurement-space, instead of the signal-space as in previous work. In this paper, we propose to modify the training strategy of end-to-end deep-learning-based inverse problem solvers to improve robustness. We introduce an auxiliary network to generate adversarial examples, which is used in a min-max formulation to build robust image reconstruction networks. Theoretically, we show for a linear reconstruction scheme the min-max formulation results in a singular-value(s) filter regularized solution, which suppresses the effect of adversarial examples occurring because of ill-conditioning in the measurement matrix. We find that a linear network using the proposed min-max learning scheme indeed converges to the same solution. In addition, for non-linear Compressed Sensing (CS) reconstruction using deep networks, we show significant improvement in robustness using the proposed approach over other methods. We complement the theory by experiments for CS on two different datasets and evaluate the effect of increasing perturbations on trained networks. We find the behavior for ill-conditioned and well-conditioned measurement matrices to be qualitatively different.
    Keywords Computer Science - Machine Learning ; Computer Science - Computer Vision and Pattern Recognition ; Statistics - Machine Learning
    Subject code 006
    Publishing date 2020-02-26
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  10. Book ; Online: A Set-Theoretic Study of the Relationships of Image Models and Priors for Restoration Problems

    Wen, Bihan / Li, Yanjun / Li, Yuqi / Bresler, Yoram

    2020  

    Abstract: Image prior modeling is the key issue in image recovery, computational imaging, compresses sensing, and other inverse problems. Recent algorithms combining multiple effective priors such as the sparse or low-rank models, have demonstrated superior ... ...

    Abstract Image prior modeling is the key issue in image recovery, computational imaging, compresses sensing, and other inverse problems. Recent algorithms combining multiple effective priors such as the sparse or low-rank models, have demonstrated superior performance in various applications. However, the relationships among the popular image models are unclear, and no theory in general is available to demonstrate their connections. In this paper, we present a theoretical analysis on the image models, to bridge the gap between applications and image prior understanding, including sparsity, group-wise sparsity, joint sparsity, and low-rankness, etc. We systematically study how effective each image model is for image restoration. Furthermore, we relate the denoising performance improvement by combining multiple models, to the image model relationships. Extensive experiments are conducted to compare the denoising results which are consistent with our analysis. On top of the model-based methods, we quantitatively demonstrate the image properties that are inexplicitly exploited by deep learning method, of which can further boost the denoising performance by combining with its complementary image models.
    Keywords Electrical Engineering and Systems Science - Image and Video Processing ; Computer Science - Machine Learning ; Electrical Engineering and Systems Science - Signal Processing ; Statistics - Machine Learning
    Subject code 006
    Publishing date 2020-03-29
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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