Related papers: A Deep Learning-Enhanced Fourier Method for the Mu…
We propose a transfer learning framework for sound source reconstruction in Near-field Acoustic Holography (NAH), which adapts a well-trained data-driven model from one type of sound source to another using a physics-informed procedure. The…
The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the…
We consider an inverse shape problem for recovering an unknown simply supported obstacle in two dimensions from near--field point--source measurements for the biharmonic Helmholtz equation. The measured data consist of the scattered field…
Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…
While neural networks have made significant strides in many AI tasks, they remain vulnerable to a range of noise types, including natural corruptions, adversarial noise, and low-resolution artifacts. Many existing approaches focus on…
This work is dedicated to uniqueness and numerical algorithms for determining the point sources of the biharmonic wave equation using scattered fields at sparse sensors. We first show that the point sources in both $\mathbb{R}^2$ and…
Inverse problems in image reconstruction are fundamentally complicated by unknown noise properties. Classical iterative deconvolution approaches amplify noise and require careful parameter selection for an optimal trade-off between…
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…
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…
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…
We present a novel method to provide efficient and highly detailed reconstructions. Inspired by wavelets, we learn a neural field that decompose the signal both spatially and frequency-wise. We follow the recent grid-based paradigm for…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
Fourier ptychography is a recently developed imaging approach for large field-of-view and high-resolution microscopy. Here we model the Fourier ptychographic forward imaging process using a convolution neural network (CNN) and recover the…
We study increasing stability in the inverse source problems for the Helmholtz equation and the classical Lame system from (minimal) boundary data at multiple wave numbers. By using the Fourier transform with respect to wave numbers,…
We propose an audio-to-audio neural network model that learns to denoise old music recordings. Our model internally converts its input into a time-frequency representation by means of a short-time Fourier transform (STFT), and processes the…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different…
Fourier phase retrieval is a classical problem of restoring a signal only from the measured magnitude of its Fourier transform. Although Fienup-type algorithms, which use prior knowledge in both spatial and Fourier domains, have been widely…