Joint reconstruction and low-rank decomposition for dynamic inverse problems

Arridge, Simon R.; Fernsel, Pascal; Hauptmann, Andreas

doi:10.3934/ipi.2021059

Cited by 8 publications

(5 citation statements)

References 45 publications

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“…In the feature fusion layer, the feature vector y1 is obtained from the nonlinear model. It is spliced with the feature vector y2 obtained from the linear model to form a fusion vector (15) Where represents the vector splicing operation. The feature vector contains both nonlinear features and linear features.…”

Section: Detail Of Fu Ntc Modelmentioning

confidence: 99%

“…The fixed-point extension and approximate singular value decomposition algorithm for solving the rank minimization problem of large-scale matrices [12] proposed by Qiao et al Ahn et al Provide a boundary for the number of elements needed to reconstruct a low-rank matrix. It is optimal in the range of a small numerical constant and a logarithmic factor [13][14][15]. In addition, some studies have shown that, under certain constraints, the minimum kernel norm can be filled by partial observation elements of the matrix [16].…”

Section: Introductionmentioning

confidence: 99%

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Quantization and application of low-rank tensor decomposition based on the deep learning model.

Zhao¹

2023

3C TIC

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Watching the presentation of a large-scale network is very important for network state tracking, performance optimization, traffic engineering, anomaly detection, fault analysis, etc. In this paper, we try to develop deep learning technology to solve the defect problem of tensor filling based on inner product interaction. To solve the limitations of the existing tensor-filling algorithms, a new neural tensor-filling (NTC) model is proposed. NTC model can effectively type the third-order communication between data landscapes through outer creation operation. It creates the third-order interaction mapping tensor. On this basis, the interaction between local features of the 3D neural network is studied. In this paper, another fusion neural tensor filling (Fu NTC) model is proposed to solve the problem that the NTC model can only extract the nonlinear complex structural information between potential feature dimensions. In the framework of the neural network, the NTC model and tensor decomposition model share the same potential feature embedding. It can effectively extract nonlinear feature information and linear feature information at the same time. It achieves higher precision data recovery.

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Section: Detail Of Fu Ntc Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantization and application of low-rank tensor decomposition based on the deep learning model.

Zhao¹

2023

3C TIC

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“…the object is to be reconstructed at a range of time points. Here, one usually has to deal with sparse data or limited angle problems [2,8,9]. Including motion, the Radon transform is now computed for a deformed version of ϑ over the whole time interval, which changes the setting to…”

Section: Introductionmentioning

confidence: 99%

Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces

Burger,

Schuster,

Wald

2024

Inverse Problems

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We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover parameters from given observations where the parameters or the data depend on time. There are various important applications being subject of current research that belong to this class of problems. Typically inverse problems are ill-posed in the sense that already small noise in the data causes tremendous errors in the solution. In this article we present two diﬀerent concepts of ill-posedness: temporally (pointwise) ill-posedness and uniform ill-posedness with respect to the Lebesgue-Bochner setting. We investigate the two concepts by means of a typical setting consisting of a time-depending observation operator composed by a compact operator. Furthermore we develop regularization methods that are adapted to the respective class of ill-posedness.

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“…For instance, in medical imaging the CT image might be used for identification and quantification of cancer tissue [11]. Thus, in recent years some researchers have also increasingly considered to combine both tasks in a joint framework [12], [13], [14]. Nevertheless, we will concentrate here on a separated approach, but keep the segmentation quality in mind as evaluation criterion of reconstruction quality rather than quantitative reconstruction errors.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction and segmentation from sparse sequential X-ray measurements of wood logs

Springer¹,

Glielmo²,

Senchukova³

et al. 2022

Preprint

Self Cite

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In industrial applications it is common to scan objects on a moving conveyor belt. If slice-wise 2D computed tomography (CT) measurements of the moving object are obtained we call it a sequential scanning geometry. In this case, each slice on its own does not carry sufficient information to reconstruct a useful tomographic image. Thus, here we propose the use of a Dimension reduced Kalman Filter to accumulate information between slices and allow for sufficiently accurate reconstructions for further assessment of the object. Additionally, we propose to use an unsupervised clustering approach known as Density Peak Advanced, to perform a segmentation and spot density anomalies in the internal structure of the reconstructed objects. We evaluate the method in a proof of concept study for the application of wood log scanning for the industrial sawing process, where the goal is to spot anomalies within the wood log to allow for optimal sawing patterns. Reconstruction and segmentation quality is evaluated from experimental measurement data for various scenarios of severely undersampled X-measurements. Results show clearly that an improvement of reconstruction quality can be obtained by employing the Dimension reduced Kalman Filter allowing to robustly obtain the segmented logs.

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Joint reconstruction and low-rank decomposition for dynamic inverse problems

Cited by 8 publications

References 45 publications

Quantization and application of low-rank tensor decomposition based on the deep learning model.

Quantization and application of low-rank tensor decomposition based on the deep learning model.

Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces

Reconstruction and segmentation from sparse sequential X-ray measurements of wood logs

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