skip to main content

Title: Reconstruction of Sparsely Sampled Seismic Data via Residual U-Net
Reconstruction of sparsely sampled seismic data is critical for maintaining the quality of seismic images when significant numbers of shots and receivers are missing.We present a reconstruction method in the shot-receiver-time (SRT) domain based on a residual U-Net machine learning architecture, for seismic data acquired in a sparse 2-D acquisition and name it SRT2D-ResU-Net. The SRT domain retains a high level of seismic signal connectivity, which is likely the main data feature that the reconstructing algorithms rely on. We develop an “in situ training and prediction” workflow by dividing the acquisition area into two nonoverlapping subareas: a training subarea for establishing the network model using regularly sampled data and a testing subarea for reconstructing the sparsely sampled data using the trained model. To establish a reference base for analyzing the changes in data features over the study area, and quantifying the reconstructed seismic data, we devise a baseline reference using a tiny portion of the field data. The baselines are properly spaced and excluded from the training and reconstruction processes. The results on a field marine data set show that the SRT2D-ResU-Net can effectively learn the features of seismic data in the training process, and the average correlation between the reconstructed missing traces and the true answers is over 85%.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
IEEE Geoscience and Remote Sensing Letters
Page Range / eLocation ID:
1 to 5
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Purpose

    To develop a scan‐specific model that estimates and corrects k‐space errors made when reconstructing accelerated MRI data.


    Scan‐specific artifact reduction in k‐space (SPARK) trains a convolutional‐neural‐network to estimate and correct k‐space errors made by an input reconstruction technique by back‐propagating from the mean‐squared‐error loss between an auto‐calibration signal (ACS) and the input technique’s reconstructed ACS. First, SPARK is applied to generalized autocalibrating partially parallel acquisitions (GRAPPA) and demonstrates improved robustness over other scan‐specific models, such as robust artificial‐neural‐networks for k‐space interpolation (RAKI) and residual‐RAKI. Subsequent experiments demonstrate that SPARK synergizes with residual‐RAKI to improve reconstruction performance. SPARK also improves reconstruction quality when applied to advanced acquisition and reconstruction techniques like 2D virtual coil (VC‐) GRAPPA, 2D LORAKS, 3D GRAPPA without an integrated ACS region, and 2D/3D wave‐encoded imaging.


    SPARK yields SSIM improvement and 1.5 – 2× root mean squared error (RMSE) reduction when applied to GRAPPA and improves robustness to ACS size for various acceleration rates in comparison to other scan‐specific techniques. When applied to advanced reconstruction techniques such as residual‐RAKI, 2D VC‐GRAPPA and LORAKS, SPARK achieves up to 20% RMSE improvement. SPARK with 3D GRAPPA also improves RMSE performance by ~2×, SSIM performance, and perceived image quality without a fully sampled ACS region. Finally, SPARK synergizes with non‐Cartesian, 2D and 3D wave‐encoding imaging by reducing RMSE between 20% and 25% and providing qualitative improvements.


    SPARK synergizes with physics‐based acquisition and reconstruction techniques to improve accelerated MRI by training scan‐specific models to estimate and correct reconstruction errors in k‐space.

    more » « less
  2. Abstract The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Specifically, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization defined on the CAUG for the resulting ill-posed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the superiority of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with the quadratic regularization, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid. 
    more » « less
  3. Deep learning has been applied to magnetic resonance imaging (MRI) for a variety of purposes, ranging from the acceleration of image acquisition and image denoising to tissue segmentation and disease diagnosis. Convolutional neural networks have been particularly useful for analyzing MRI data due to the regularly sampled spatial and temporal nature of the data. However, advances in the field of brain imaging have led to network- and surface-based analyses that are often better represented in the graph domain. In this analysis, we propose a general purpose cortical segmentation method that, given resting-state connectivity features readily computed during conventional MRI pre-processing and a set of corresponding training labels, can generate cortical parcellations for new MRI data. We applied recent advances in the field of graph neural networks to the problem of cortical surface segmentation, using resting-state connectivity to learn discrete maps of the human neocortex. We found that graph neural networks accurately learn low-dimensional representations of functional brain connectivity that can be naturally extended to map the cortices of new datasets. After optimizing over algorithm type, network architecture, and training features, our approach yielded mean classification accuracies of 79.91% relative to a previously published parcellation. We describe how some hyperparameter choices including training and testing data duration, network architecture, and algorithm choice affect model performance. 
    more » « less
  4. We present a new method to obtain dynamic body force at virtual interfaces to reconstruct shear wave motions induced by a source outside a truncated computational domain. Specifically, a partial differential equation (PDE)-constrained optimization method is used to minimize the misfit between measured motions at a limited number of sensors on the ground surface and their counterparts reconstructed from optimized forces. Numerical results show that the optimized forces accurately reconstruct the targeted ground motions in the surface and the interior of the domain. The proposed optimization framework yields a particular force vector among other valid solutions allowed by the domain reduction method (DRM). Per this optimized or inverted force vector, the reconstructed wave field is identical to its reference counterpart in the domain of interest but may differ in the exterior domain from the reference one. However, we remark that the inverted solution is valid and introduce a simple post-process that can modify the solution to achieve an alternative force vector corresponding to the reference wave field. We also study the desired sensor spacing to accurately reconstruct the wave responses for a given dominant frequency of interest. We remark that the presented method is omnidirectionally applicable in terms of the incident angle of an incoming wave and is effective for any given material heterogeneity and geometry of layering of a reduced domain. The presented inversion method requires information on the wave speeds and dimensions of only a reduced domain. Namely, it does not need any informa- tion on the geophysical profile of an enlarged domain or a seismic source profile outside a reduced domain. Thus, the computational cost of the method is compact even though it leads to the high-fidelity reconstruction of wave re- sponse in the reduced domain, allowing for studying and predicting ground and structural responses using real seismic measurements. 
    more » « less
  5. Abstract

    Existing applications of deep learning in computational imaging and microscopy mostly depend on supervised learning, requiring large-scale, diverse and labelled training data. The acquisition and preparation of such training image datasets is often laborious and costly, leading to limited generalization to new sample types. Here we report a self-supervised learning model, termed GedankenNet, that eliminates the need for labelled or experimental training data, and demonstrate its effectiveness and superior generalization on hologram reconstruction tasks. Without prior knowledge about the sample types, the self-supervised learning model was trained using a physics-consistency loss and artificial random images synthetically generated without any experiments or resemblance to real-world samples. After its self-supervised training, GedankenNet successfully generalized to experimental holograms of unseen biological samples, reconstructing the phase and amplitude images of different types of object using experimentally acquired holograms. Without access to experimental data, knowledge of real samples or their spatial features, GedankenNet achieved complex-valued image reconstructions consistent with the wave equation in free space. The GedankenNet framework also shows resilience to random, unknown perturbations in the physical forward model, including changes in the hologram distances, pixel size and illumination wavelength. This self-supervised learning of image reconstruction creates new opportunities for solving inverse problems in holography, microscopy and computational imaging.

    more » « less