Related papers: From constant to variable density inverse extended…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
State-of-the-art learned reconstruction methods often rely on black-box modules that, despite their strong performance, raise questions about their interpretability and robustness. Here, we build on a recently proposed image reconstruction…
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…
We study the problem of multi-compression and reconstructing a stochastic signal observed by several independent sensors (or compressors) that transmit compressed information to a fusion center. { The key aspect of this problem is to find…
This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…
We analyze the convergence and approximation error of the inverse Born series, obtaining results that hold under qualitatively weaker conditions than previously known. Our approach makes use of tools from geometric function theory in Banach…
We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…
We introduce a novel nonlinear imaging method for the acoustic wave equation based on data-driven model order reduction. The objective is to image the discontinuities of the acoustic velocity, a coefficient of the scalar wave equation from…
The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…
Robust regression techniques rely on least-squares optimization, which works well for Gaussian noise but fails in the presence of asymmetric structured noise. We propose a hybrid neural-symbolic architecture where a transformer encoder…
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
A feature-mapping framework for inverse reconstruction of density-based topology optimization results is proposed. Unlike SIMP, whose voxelized outputs are hard to interpret or reuse, the method represents designs with high-level geometric…
This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…