相关论文: FFT Interpolation from Nonuniform Samples Lying in…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…

The Fast Fourier Transform (FFT) is a fundamental tool for signal analysis, widely used across various fields. However, traditional FFT methods encounter challenges in adjusting the frequency bin interval, which may impede accurate spectral…

Sparse regularization is a central technique for both machine learning (to achieve supervised features selection or unsupervised mixture learning) and imaging sciences (to achieve super-resolution). Existing performance guaranties assume a…

Low-count positron emission tomography (PET) reconstruction is a challenging inverse problem due to severe degradations arising from Poisson noise, photon scarcity, and attenuation correction errors. Existing deep learning methods typically…

Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…

The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis to decompose the signal is not…

This paper is concerned with the inverse problem of determining the shape of penetrable periodic scatterers from scattered field data. We propose a sampling method with a novel indicator function for solving this inverse problem. This…

Periodicity analysis of unevenly collected data is a relevant issue in several scientific fields. In astrophysics, for example, we have to find the fundamental period of light or radial velocity curves which are unevenly sampled…

This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…

We consider how some methods of uniform and nonuniform interpolation by translates of radial basis functions -- specifically the so-called general multiquadrics -- perform in the presence of certain types of noise. These techniques provide…

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce…

In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…

For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…

The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…

Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…

We present an algorithm based on numerical techniques that have become standard for solving nonlinear integral equations: Newton's method, homotopy continuation, the multilevel method and random projection to solve the inversion problem…