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We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed that is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
In this paper, we propose a novel approach that harnesses the standard interference function, specifically tailored to address the unique challenges of non-convex optimization in wireless networks. We begin by establishing theoretical…
Variational method and deep learning method are two mainstream powerful approaches to solve inverse problems in computer vision. To take advantages of advanced optimization algorithms and powerful representation ability of deep neural…
Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as…
A range of nonlinear image reconstruction procedures based on extremizing the generalized Shannon entropy, Kullback-Leibler cross-entropy and Renyi information measures and proposed by the author in early papers is presented. The…
In this paper, we consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. Specifically, we treat sensing problems with model mismatch where one wishes to recover a sparse…
Ultrasonic guided wave technology has played a significant role in the field of non-destructive testing as it employs acoustic waves that have advantages of high propagation efficiency and low energy consumption during the inspect process.…
We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Purpose: This work aims at developing a generalizable MRI reconstruction model in the meta-learning framework. The standard benchmarks in meta-learning are challenged by learning on diverse task distributions. The proposed network learns…
We use Ikehata's enclosure method to reconstruct penetrable unknown inclusions in a plane elastic body in time-harmonic waves. Complex geometrical optics solutions with complex polynomial phases are adopted as the probing utility. In a…
Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
We propose a coherent method for the detection and reconstruction of gravitational wave signals for a network of interferometric detectors. The method is derived using the likelihood functional for unknown signal waveforms. In the standard…
We propose an unrolled algorithm approach for learning spatially adaptive parameter maps in the framework of convolutional synthesis-based $\ell_1$ regularization. More precisely, we consider a family of pre-trained convolutional filters…
This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…
In this paper, we show that using measurements for different frequencies, and using ultrasound localized perturbations it is possible to extend the method of the imaging by elastic deformation developed by Ammari and al. [Electrical…
We consider the so-called unfolding problem in experimental high energy physics, where the goal is to estimate the true spectrum of elementary particles given observations distorted by measurement error due to the limited resolution of a…