Related papers: Wavelets and sparsity for Faraday tomography
In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…
Polarized synchrotron emission from multiple Faraday depths can be separated by calculating the complex Fourier transform of the Stokes' parameters as a function of the wavelength squared, known as Faraday Synthesis. As commonly…
We introduce a dual-wavelength Fourier ptychographic topography (FPT) method that extends the lambda/2 height-range limit of single-wavelength FPT. By reconstructing complex fields at two illumination wavelengths and exploiting their phase…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…
The new generation of low-frequency radio telescopes, such as the Low Frequency Array (LOFAR: a Square Kilometre Array-low pathfinder), provides advancements in our capability of probing Galactic magnetism through low-frequency polarimetry.…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…
This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…
Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets…
This paper aims to address a common challenge in deep learning-based image transformation methods, such as image enhancement and super-resolution, which heavily rely on precisely aligned paired datasets with pixel-level alignments. However,…
Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the…
Magnetic Faraday rotation is widely used in optics and MW. In uniform magneto-optical materials, this effect is very weak. One way to enhance it is to incorporate the magnetic material into a high-Q optical resonator. One problem with…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
We propose a formulation of full-wavefield inversion (FWI) as a constrained optimization problem, and describe a computationally efficient technique for solving constrained full-wavefield inversion (CFWI). The technique is based on using a…
This paper studies the problem of sampling vector and tensor signals, which is the process of choosing sites in vectors and tensors to place sensors for better recovery. A small core tensor and multiple factor matrices can be used to…
Instead of directly utilizing an observed image including some outliers, noise or intensity inhomogeneity, the use of its ideal value (e.g. noise-free image) has a favorable impact on clustering. Hence, the accurate estimation of the…
Radio broadband spectro-polarimetric observations are sensitive to the spatial fluctuations of the Faraday depth (FD) within the telescope beam. Such FD fluctuations are referred to as "Faraday complexity", and can unveil small-scale…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…