Enhancing joint reconstruction and segmentation with non-convex Bregman iteration

Corona, Veronica; Benning, Martin; Ehrhardt, Matthias J.; Gladden, Lynn F.; Mair, Richard; Reci, Andi; Sederman, Andrew J.; Reichelt, Stefanie; Schönlieb, Carola-Bibiane

doi:10.1088/1361-6420/ab0b77

Cited by 23 publications

(17 citation statements)

References 48 publications

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“…For example, when the image is noisy, blurred, has regions missing, or we observe only a transform of the image, such as the output of a CT or MRI scanner. “Joint reconstruction and segmentation” (see [1, 17]) is the task of simultaneously reconstructing and segmenting an image, which can reduce computational time and improve the quality of both the reconstruction and the segmentation.…”

Section: Resultsmentioning

confidence: 99%

Classification and image processing with a semi‐discrete scheme for fidelity forced Allen–Cahn on graphs

2021

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This paper introduces a semi‐discrete implicit Euler (SDIE) scheme for the Allen‐Cahn equation (ACE) with fidelity forcing on graphs. The continuous‐in‐time version of this differential equation was pioneered by Bertozzi and Flenner in 2012 as a method for graph classification problems, such as semi‐supervised learning and image segmentation. In 2013, Merkurjev et. al. used a Merriman‐Bence‐Osher (MBO) scheme with fidelity forcing instead, as heuristically it was expected to give similar results to the ACE. The current paper rigorously establishes the graph MBO scheme with fidelity forcing as a special case of an SDIE scheme for the graph ACE with fidelity forcing. This connection requires the use of the double‐obstacle potential in the ACE, as was already demonstrated by Budd and Van Gennip in 2020 in the context of ACE without a fidelity forcing term. We also prove that solutions of the SDIE scheme converge to solutions of the graph ACE with fidelity forcing as the discrete time step converges to zero. In the second part of the paper we develop the SDIE scheme as a classification algorithm. We also introduce some innovations into the algorithms for the SDIE and MBO schemes. For large graphs, we use a QR decomposition method to compute an eigendecomposition from a Nyström extension, which outperforms the method used by, for example, Bertozzi and Flenner in 2012, in accuracy, stability, and speed. Moreover, we replace the Euler discretization for the scheme's diffusion step by a computation based on the Strang formula for matrix exponentials. We apply this algorithm to a number of image segmentation problems, and compare the performance with that of the graph MBO scheme with fidelity forcing. We find that while the general SDIE scheme does not perform better than the MBO special case at this task, our other innovations lead to a significantly better segmentation than that from previous literature. We also empirically quantify the uncertainty that this segmentation inherits from the randomness in the Nyström extension.

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Section: Resultsmentioning

confidence: 99%

Classification and image processing with a semi‐discrete scheme for fidelity forced Allen–Cahn on graphs

2021

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“…In such a case, additional constraints can be naturally added to ensure smoothness and continuity of the identified boundaries between different geological units. The versatility of such solvers has recently led to the creation of a novel joint reconstruction and segmentation algorithm in the context of medical imaging Corona et al (2019) that we seek to adapt to the problem of seismic inversion.…”

Section: O R I Gmentioning

confidence: 99%

“…Inspired by the work of Corona et al (2019) on joint reconstruction and segmentation in the context of medical imaging, we define a functional to invert seismic data for their acoustic impedance as well as to produce a segmentation of the subsurface into N c classes, each of which is associated with a specific range of impedance values. The underlying idea of inverting for these two parameters simultaneously is to inform the inversion with prior knowledge about the rock units of interest, whilst at the same time constraining this belief with the seismic measurements.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Segmentation of Seismic data 33 inverse problem. Apart from some specific cases involving orthogonal operators, where an analytical solution can be identified (e.g., CT scan reconstruction -Corona et al (2019)), the evaluation of such an operator is generally the most expensive of the operators involved in our algorithm and requires the use of iterative solvers (e.g., CGLS, LSQR). However, as each iteration of the Primal-Dual algorithm represents only a step towards the saddle point of the corresponding Primal-Dual functional,…”

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confidence: 99%

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A joint inversion-segmentation approach to assisted seismic interpretation

Ravasi

Birnie

2021

Geophysical Journal International

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Summary Structural seismic interpretation and quantitative characterization are historically intertwined processes. The latter provides estimates of the properties of the subsurface, which can be used to aid structural interpretation alongside the original seismic data and a number of other seismic attributes. In this work, we redefine this process as an inverse problem which tries to jointly estimate subsurface properties (i.e., acoustic impedance) and a piece-wise segmented representation of the subsurface based on user-defined macro-classes. By inverting for the quantities simultaneously, the inversion is primed with prior knowledge about the regions of interest, whilst at the same time it constrains this belief with the actual seismic measurements. As the proposed functional is separable in the two quantities, these are optimized in an alternating fashion, where each subproblem is solved using the Primal-Dual algorithm. Subsequently, the final segmented model is used as input to an ad-hoc workflow that extracts the perimeter of the detected shapes and produces a structural framework (i.e., seismic horizons) consistent with the estimated subsurface properties. The effectiveness of the proposed method is illustrated through numerical examples on synthetic and field datasets.

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“…Recently, solving the reconstruction and segmentation problem jointly has become increasingly popular: by treating both problems simultaneously, reconstruction can benefit from information available in the segmentation and vice versa. One such method is given in [40], which also contains an overview on other non-learned joint methods. A recent work in which the segmentation is jointly solved with motionestimation in an unsupervised learning approach is given in [41].…”

Section: Introductionmentioning

confidence: 99%

A Partially-Learned Algorithm for Joint Photo-acoustic Reconstruction and Segmentation

Boink

Manohar

Brüne

2020

IEEE Trans. Med. Imaging

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In an inhomogeneously illuminated photoacoustic image, important information like vascular geometry is not readily available when only the initial pressure is reconstructed. To obtain the desired information, algorithms for image segmentation are often applied as a post-processing step. In this work, we propose to jointly acquire the photoacoustic reconstruction and segmentation, by modifying a recently developed partially learned algorithm based on a convolutional neural network. We investigate the stability of the algorithm against changes in initial pressures and photoacoustic system settings. These insights are used to develop an algorithm that is robust to input and system settings. Our approach can easily be applied to other imaging modalities and can be modified to perform other high-level tasks different from segmentation. The method is validated on challenging synthetic and experimental photoacoustic tomography data in limited angle and limited view scenarios. It is computationally less expensive than classical iterative methods and enables higher quality reconstructions and segmentations than state-of-the-art learned and non-learned methods.

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Enhancing joint reconstruction and segmentation with non-convex Bregman iteration

Cited by 23 publications

References 48 publications

Classification and image processing with a semi‐discrete scheme for fidelity forced Allen–Cahn on graphs

Classification and image processing with a semi‐discrete scheme for fidelity forced Allen–Cahn on graphs

A joint inversion-segmentation approach to assisted seismic interpretation

A Partially-Learned Algorithm for Joint Photo-acoustic Reconstruction and Segmentation

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