Related papers: Transcending Sparse Measurement Limits: Operator-L…

We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…

We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…

Transfer Learning aims to optimally aggregate samples from a target distribution, with related samples from a so-called source distribution to improve target risk. Multiple procedures have been proposed over the last two decades to address…

This paper investigates the inverse source problem with a single propagating mode at multiple frequencies in an acoustic waveguide. The goal is to provide both theoretical justifications and efficient algorithms for imaging extended sources…

With the abundance of industrial datasets, imbalanced classification has become a common problem in several application domains. Oversampling is an effective method to solve imbalanced classification. One of the main challenges of the…

Many computer vision systems require low-cost segmentation algorithms based on deep learning, either because of the enormous size of input images or limited computational budget. Common solutions uniformly downsample the input images to…

Despite over two decades of progress, imbalanced data is still considered a significant challenge for contemporary machine learning models. Modern advances in deep learning have magnified the importance of the imbalanced data problem. The…

We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the…

Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the…

Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…

Recent advances in deep neural networks (DNNs) owe their success to training algorithms that use backpropagation and gradient-descent. Backpropagation, while highly effective on von Neumann architectures, becomes inefficient when scaling to…

For massive multiple-input multiple-output (MIMO) systems operating in frequency-division duplex mode, downlink channel state information (CSI) acquisition will incur large overhead. This overhead is substantially reduced when sparse…

The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is…

A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…

We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz equation, where the subdomain problems satisfy first-order absorbing (impedance) transmission conditions, and exchange of information between subdomains…

Compressive sensing has been successfully used for optimized operations in wireless sensor networks. However, raw data collected by sensors may be neither originally sparse nor easily transformed into a sparse data representation. This…

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…

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been…

In this paper we consider the problem of localizing a set of broadband sources from a finite window of measurements. In the case of narrowband sources this can be reduced to the problem of spectral line estimation, where our goal is simply…