arXiv subjects

Brendt Wohlberg

Publications and source records attributed to Brendt Wohlberg.

At least 37 records · Page 2Linked to original sources

arXiv2023

Coordinate-Based Seismic Interpolation in Irregular Land Survey: A Deep Internal Learning Approach

Physical and budget constraints often result in irregular sampling, which complicates accurate subsurface imaging. Pre-processing approaches, such as missing trace or shot interpolation, are typically employed to enhance seismic data in such cases. Recently, deep learning has been used to address the trace interpolation problem at the expense of large amounts of training data to adequately represent typical seismic events. Nonetheless, most research in this area has focused on trace reconstruction, with little attention having been devoted to shot interpolation. Furthermore, existing methods assume regularly spaced receivers/sources failing in approximating seismic data from real (irregular) surveys. This work presents a novel shot gather interpolation approach which uses a continuous coordinate-based representation of the acquired seismic wavefield parameterized by a neural network. The proposed unsupervised approach, which we call coordinate-based seismic interpolation(CoBSI), enables the prediction of specific seismic characteristics in irregular land surveys without using external data during neural network training. Experimental results on real and synthetic 3D data validate the ability of the proposed method to estimate continuous smooth seismic events in the time-space and frequency-wavenumber domains, improving sparsity or low-rank-based interpolation methods.

eess.IV↗

arXiv2022

Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging

Plug-and-Play Priors (PnP) is one of the most widely-used frameworks for solving computational imaging problems through the integration of physical models and learned models. PnP leverages high-fidelity physical sensor models and powerful machine learning methods for prior modeling of data to provide state-of-the-art reconstruction algorithms. PnP algorithms alternate between minimizing a data-fidelity term to promote data consistency and imposing a learned regularizer in the form of an image denoiser. Recent highly-successful applications of PnP algorithms include bio-microscopy, computerized tomography, magnetic resonance imaging, and joint ptycho-tomography. This article presents a unified and principled review of PnP by tracing its roots, describing its major variations, summarizing main results, and discussing applications in computational imaging. We also point the way towards further developments by discussing recent results on equilibrium equations that formulate the problem associated with PnP algorithms.

eess.IV↗

arXiv2022

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. This report summarizes the outcomes of that workshop, "Randomized Algorithms for Scientific Computing (RASC)," held virtually across four days in December 2020 and January 2021.

cs.AI↗

arXiv2021

Projected Multi-Agent Consensus Equilibrium for Ptychographic Image Reconstruction

Ptychography is a computational imaging technique using multiple, overlapping, coherently illuminated snapshots to achieve nanometer resolution by solving a nonlinear phase-field recovery problem. Ptychography is vital for imaging of manufactured nanomaterials, but existing algorithms have computational shortcomings that limit large-scale application. In this paper, we present the Projected Multi-Agent Consensus Equilibrium (PMACE) approach for solving the ptychography inversion problem. This approach extends earlier work on MACE, which formulates an inversion problem as an equilibrium among multiple agents, each acting independently to update a full reconstruction. In PMACE, each agent acts on a portion (projection) corresponding to one of the snapshots, and these updates to projections are then combined to give an update to the full reconstruction. The resulting algorithm is easily parallelized, with convergence properties inherited from convergence results associated with MACE. We apply our method on simulated data and demonstrate that it outperforms competing algorithms in both reconstruction quality and convergence speed.

eess.IV↗

arXiv2021

InversionNet3D: Efficient and Scalable Learning for 3D Full Waveform Inversion

Seismic full-waveform inversion (FWI) techniques aim to find a high-resolution subsurface geophysical model provided with waveform data. Some recent effort in data-driven FWI has shown some encouraging results in obtaining 2D velocity maps. However, due to high computational complexity and large memory consumption, the reconstruction of 3D high-resolution velocity maps via deep networks is still a great challenge. In this paper, we present InversionNet3D, an efficient and scalable encoder-decoder network for 3D FWI. The proposed method employs group convolution in the encoder to establish an effective hierarchy for learning information from multiple sources while cutting down unnecessary parameters and operations at the same time. The introduction of invertible layers further reduces the memory consumption of intermediate features during training and thus enables the development of deeper networks with more layers and higher capacity as required by different application scenarios. Experiments on the 3D Kimberlina dataset demonstrate that InversionNet3D achieves state-of-the-art reconstruction performance with lower computational cost and lower memory footprint compared to the baseline.

cs.LG↗

arXiv2021

Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition

The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixed-points of a deep neural network. We also present numerical results comparing the recovery performance of PnP/RED in compressive sensing against that of recent compressive sensing algorithms based on generative models. Our numerical results suggest that PnP with a pre-trained artifact removal network provides significantly better results compared to the existing state-of-the-art methods.

cs.CV↗

arXiv2021

Hyperspectral Neutron CT with Material Decomposition

Energy resolved neutron imaging (ERNI) is an advanced neutron radiography technique capable of non-destructively extracting spatial isotopic information within a given material. Energy-dependent radiography image sequences can be created by utilizing neutron time-of-flight techniques. In combination with uniquely characteristic isotopic neutron cross-section spectra, isotopic areal densities can be determined on a per-pixel basis, thus resulting in a set of areal density images for each isotope present in the sample. By preforming ERNI measurements over several rotational views, an isotope decomposed 3D computed tomography is possible. We demonstrate a method involving a robust and automated background estimation based on a linear programming formulation. The extremely high noise due to low count measurements is overcome using a sparse coding approach. It allows for a significant computation time improvement, from weeks to a few hours compared to existing neutron evaluation tools, enabling at the present stage a semi-quantitative, user-friendly routine application.

eess.IV↗

arXiv2021

Connect the Dots: In Situ 4D Seismic Monitoring of CO2 Storage with Spatio-temporal CNNs

4D seismic imaging has been widely used in CO$_2$ sequestration projects to monitor the fluid flow in the volumetric subsurface region that is not sampled by wells. Ideally, real-time monitoring and near-future forecasting would provide site operators with great insights to understand the dynamics of the subsurface reservoir and assess any potential risks. However, due to obstacles such as high deployment cost, availability of acquisition equipment, exclusion zones around surface structures, only very sparse seismic imaging data can be obtained during monitoring. That leads to an unavoidable and growing knowledge gap over time. The operator needs to understand the fluid flow throughout the project lifetime and the seismic data are only available at a limited number of times. This is insufficient for understanding the reservoir behavior. To overcome those challenges, we have developed spatio-temporal neural-network-based models that can produce high-fidelity interpolated or extrapolated images effectively and efficiently. Specifically, our models are built on an autoencoder, and incorporate the long short-term memory (LSTM) structure with a new loss function regularized by optical flow. We validate the performance of our models using real 4D post-stack seismic imaging data acquired at the Sleipner CO$_2$ sequestration field. We employ two different strategies in evaluating our models. Numerically, we compare our models with different baseline approaches using classic pixel-based metrics. We also conduct a blind survey and collect a total of 20 responses from domain experts to evaluate the quality of data generated by our models. Via both numerical and expert evaluation, we conclude that our models can produce high-quality 2D/3D seismic imaging data at a reasonable cost, offering the possibility of real-time monitoring or even near-future forecasting of the CO$_2$ storage reservoir.

physics.geo-ph↗

arXiv2021

CoIL: Coordinate-based Internal Learning for Imaging Inverse Problems

We propose Coordinate-based Internal Learning (CoIL) as a new deep-learning (DL) methodology for the continuous representation of measurements. Unlike traditional DL methods that learn a mapping from the measurements to the desired image, CoIL trains a multilayer perceptron (MLP) to encode the complete measurement field by mapping the coordinates of the measurements to their responses. CoIL is a self-supervised method that requires no training examples besides the measurements of the test object itself. Once the MLP is trained, CoIL generates new measurements that can be used within a majority of image reconstruction methods. We validate CoIL on sparse-view computed tomography using several widely-used reconstruction methods, including purely model-based methods and those based on DL. Our results demonstrate the ability of CoIL to consistently improve the performance of all the considered methods by providing high-fidelity measurement fields.

eess.IV↗

arXiv2021

PSF Estimation in Crowded Astronomical Imagery as a Convolutional Dictionary Learning Problem

We present a new algorithm for estimating the Point Spread Function (PSF) in wide-field astronomical images with extreme source crowding. Robust and accurate PSF estimation in crowded astronomical images dramatically improves the fidelity of astrometric and photometric measurements extracted from wide-field sky monitoring imagery. Our radically new approach utilizes convolutional sparse representations to model the continuous functions involved in the image formation. This approach avoids the need to detect and precisely localize individual point sources that is shared by existing methods. In experiments involving simulated astronomical imagery, it significantly outperforms the recent alternative method with which it is compared.

eess.IV↗

arXiv2021

Scalable Plug-and-Play ADMM with Convergence Guarantees

Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the state-of-the-art performance of PnP algorithms using pre-trained deep neural nets as denoisers in a number of imaging applications. However, current PnP algorithms are impractical in large-scale settings due to their heavy computational and memory requirements. This work addresses this issue by proposing an incremental variant of the widely used PnP-ADMM algorithm, making it scalable to large-scale datasets. We theoretically analyze the convergence of the algorithm under a set of explicit assumptions, extending recent theoretical results in the area. Additionally, we show the effectiveness of our algorithm with nonsmooth data-fidelity terms and deep neural net priors, its fast convergence compared to existing PnP algorithms, and its scalability in terms of speed and memory.

cs.LG↗

arXiv2021

SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees

Deep unfolding networks have recently gained popularity in the context of solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our numerical results on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the batch network at a fraction of training and testing complexity.

eess.IV↗

arXiv2020

Joint Reconstruction and Calibration using Regularization by Denoising

Regularization by denoising (RED) is a broadly applicable framework for solving inverse problems by using priors specified as denoisers. While RED has been shown to provide state-of-the-art performance in a number of applications, existing RED algorithms require exact knowledge of the measurement operator characterizing the imaging system, limiting their applicability in problems where the measurement operator has parametric uncertainties. We propose a new method, called Calibrated RED (Cal-RED), that enables joint calibration of the measurement operator along with reconstruction of the unknown image. Cal-RED extends the traditional RED methodology to imaging problems that require the calibration of the measurement operator. We validate Cal-RED on the problem of image reconstruction in computerized tomography (CT) under perturbed projection angles. Our results corroborate the effectiveness of Cal-RED for joint calibration and reconstruction using pre-trained deep denoisers as image priors.

eess.IV↗

arXiv2020

Async-RED: A Provably Convergent Asynchronous Block Parallel Stochastic Method using Deep Denoising Priors

Regularization by denoising (RED) is a recently developed framework for solving inverse problems by integrating advanced denoisers as image priors. Recent work has shown its state-of-the-art performance when combined with pre-trained deep denoisers. However, current RED algorithms are inadequate for parallel processing on multicore systems. We address this issue by proposing a new asynchronous RED (ASYNC-RED) algorithm that enables asynchronous parallel processing of data, making it significantly faster than its serial counterparts for large-scale inverse problems. The computational complexity of ASYNC-RED is further reduced by using a random subset of measurements at every iteration. We present complete theoretical analysis of the algorithm by establishing its convergence under explicit assumptions on the data-fidelity and the denoiser. We validate ASYNC-RED on image recovery using pre-trained deep denoisers as priors.

eess.IV↗

arXiv2020

Physics-Consistent Data-driven Waveform Inversion with Adaptive Data Augmentation

Seismic full-waveform inversion (FWI) is a nonlinear computational imaging technique that can provide detailed estimates of subsurface geophysical properties. Solving the FWI problem can be challenging due to its ill-posedness and high computational cost. In this work, we develop a new hybrid computational approach to solve FWI that combines physics-based models with data-driven methodologies. In particular, we develop a data augmentation strategy that can not only improve the representativity of the training set but also incorporate important governing physics into the training process and therefore improve the inversion accuracy. To validate the performance, we apply our method to synthetic elastic seismic waveform data generated from a subsurface geologic model built on a carbon sequestration site at Kimberlina, California. We compare our physics-consistent data-driven inversion method to both purely physics-based and purely data-driven approaches and observe that our method yields higher accuracy and greater generalization ability.

cs.LG↗

arXiv2020

Provable Convergence of Plug-and-Play Priors with MMSE denoisers

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

eess.SP↗

arXiv2020

Diagram Image Retrieval using Sketch-Based Deep Learning and Transfer Learning

Resolution of the complex problem of image retrieval for diagram images has yet to be reached. Deep learning methods continue to excel in the fields of object detection and image classification applied to natural imagery. However, the application of such methodologies applied to binary imagery remains limited due to lack of crucial features such as textures,color and intensity information. This paper presents a deep learning based method for image-based search for binary patent images by taking advantage of existing large natural image repositories for image search and sketch-based methods (Sketches are not identical to diagrams, but they do share some characteristics; for example, both imagery types are gray scale (binary), composed of contours, and are lacking in texture). We begin by using deep learning to generate sketches from natural images for image retrieval and then train a second deep learning model on the sketches. We then use our small set of manually labeled patent diagram images via transfer learning to adapt the image search from sketches of natural images to diagrams. Our experiment results show the effectiveness of deep learning with transfer learning for detecting near-identical copies in patent images and querying similar images based on content.

cs.CV↗

arXiv2020

TGGLines: A Robust Topological Graph Guided Line Segment Detector for Low Quality Binary Images

Line segment detection is an essential task in computer vision and image analysis, as it is the critical foundation for advanced tasks such as shape modeling and road lane line detection for autonomous driving. We present a robust topological graph guided approach for line segment detection in low quality binary images (hence, we call it TGGLines). Due to the graph-guided approach, TGGLines not only detects line segments, but also organizes the segments with a line segment connectivity graph, which means the topological relationships (e.g., intersection, an isolated line segment) of the detected line segments are captured and stored; whereas other line detectors only retain a collection of loose line segments. Our empirical results show that the TGGLines detector visually and quantitatively outperforms state-of-the-art line segment detection methods. In addition, our TGGLines approach has the following two competitive advantages: (1) our method only requires one parameter and it is adaptive, whereas almost all other line segment detection methods require multiple (non-adaptive) parameters, and (2) the line segments detected by TGGLines are organized by a line segment connectivity graph.

cs.CV↗