Related papers: Sampling linear inverse problems with noise
Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
1/f noise is very common but is difficult to handle in a metrological way. After having recalled the main characteristics of stongly correlated noise, this paper will determine relationships giving confidence intervals over the arithmetic…
We develop a system for measurements of power spectra of transmitted light intensity fluctuations, in which the extraneous noise, including shot noise, is reduced. In essence, we just apply light, measure the power of the transmitted light…
It is well known that the class of rotation invariant algorithms are suboptimal even for learning sparse linear problems when the number of examples is below the "dimension" of the problem. This class includes any gradient descent trained…
Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the…
We study inverse problems F(f) = g with perturbed right hand side g^{obs} corrupted by so-called impulsive noise, i.e. noise which is concentrated on a small subset of the domain of definition of g. It is well known that Tikhonov-type…
The frequency dependence of the equilibrium ac conductance (or the noise power spectrum) through a mesoscopic structure is shown to exhibit steps and dips. The steps, at energies related to the resonances of the structure, are closely…
In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated…
The inverse problem methodology is a commonly-used framework in the sciences for parameter estimation and inference. It is typically performed by fitting a mathematical model to noisy experimental data. There are two significant sources of…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…
In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…
The amplification obtained using weak values is quantified through a detailed investigation of the signal to noise ratio for an optical beam deflection measurement. We show that for a given deflection, input power and beam radius, the use…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
In this paper we consider the inverse problem of vibro-acoustography, a technique for enhancing ultrasound imaging by making use of nonlinear effects. It amounts to determining two spatially variable coefficients in a system of PDEs…
Extraneous motion of optical elements in an interferometer lead to excess noise. Typically, fluctuations in the effective path length lead to phase noise, while beam-pointing leads to apparent amplitude noise. For a transmissive optic…
We look at continuum solutions in optimisation problems associated to linear inverse problems $y = Ax$ with non-negativity constraint $x \geq 0$. We focus on the case where the noise model leads to maximum likelihood estimation through…
Through a series of extensive system simulations we show that all of the previously not understood discrepancies between the Gaussian noise (GN) model and simulations can be attributed to the omission of an important, recently reported,…
Phonon dispersion of detwinned NiO is measured using inelastic x-ray scattering. It is found that, near the zone center, the energy of the transverse optical phonon mode polarized parallel to the antiferromagnetic order is ~1 meV lower than…