Related papers: A Bayesian framework for spectral reprojection
Gaussian splatting has achieved impressive improvements for both novel-view synthesis and surface reconstruction from multi-view images. However, current methods still struggle to reconstruct high-quality surfaces from only sparse view…
Multiplicative noise models occur in the study of several coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. This type of noise is also commonly referred to as speckle. Multiplicative…
Quantized compressive sensing (QCS) deals with the problem of representing compressive signal measurements with finite precision representation, i.e., a mandatory process in any practical sensor design. To characterize the signal…
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…
Fourier series approximations of continuous but nonperiodic functions on an interval suffer the Gibbs phenomenon, which means there is a permanent oscillatory overshoot in the neighbourhoods of the endpoints. Fourier extensions circumvent…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
We report the results of an in-depth analysis of the parameter estimation capabilities of BayesWave, an algorithm for the reconstruction of gravitational-wave signals without reference to a specific signal model. Using binary black hole…
Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid…
X-ray computed tomography (CT) reveals the materials' internal structures non-destructively from a tilt series of projected images. Filtered back projection (FBP) is a widely-adopted reconstruction algorithm in CT owing to its small…
In this paper, we analyze the convergence %semi-convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution to large linear, usually both noisy and ill-conditioned, systems of…
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 optimal reconstruction of cosmic metric perturbations and other signals requires knowledge of their power spectra and other parameters. If these are not known a priori, they have to be measured simultaneously from the same data used for…
Recent advances in optimizing Gaussian Splatting for scene geometry have enabled efficient reconstruction of detailed surfaces from images. However, when input views are sparse, such optimization is prone to overfitting, leading to…
Channeled spectropolarimetry measures the spectrally resolved Stokes parameters. A key aspect of this technique is to accurately reconstruct the Stokes parameters from a modulated measurement of the channeled spectropolarimeter. The…
Inverse scattering aims to infer information about a hidden object by using the received scattered waves and training data collected from forward mathematical models. Recent advances in computing have led to increasing attention towards…
Signal inpainting is the task of restoring degraded or missing samples in a signal. In this paper we address signal inpainting when Fourier magnitudes are observed. We propose a mathematical formulation of the problem that highlights its…
In this paper, we consider the problem of reconstructing piece-wise smooth functions from their non-uniform Fourier data. We first extend the filter method for uniform Fourier data to the non-uniform setting by using the techniques of…
Inverse rendering of glossy objects from RGB imagery remains fundamentally limited by inherent ambiguity. Although NeRF-based methods achieve high-fidelity reconstruction via dense-ray sampling, their computational cost is prohibitive.…