相关论文: Pole recovery from noisy data on imaginary axis

We present a method able to recover location and residue of poles of functions meromorphic in a half--plane from samples of the function on the real positive semi-axis. The function is assumed to satisfy appropriate asymptotic conditions…

On the basis of the generalized argument principle, here we develop a numerical scheme for locating zeros and poles of a meromorphic function. A subdivision-transformation-calculation scheme is proposed to ensure the algorithm stability. A…

In this paper, we show that sparse signals f representable as a linear combination of a finite number N of spikes at arbitrary real locations or as a finite linear combination of B-splines of order m with arbitrary real knots can be almost…

We propose a method based on minimum-variance polynomial approximation to extract system poles from a data set of samples of the impulse response of a linear system. The method is capable of handling the problem under general conditions of…

The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…

A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…

Extracting environmental forces from noisy data is a common yet challenging task in complex physical systems. Machine learning represents a robust approach to this problem, yet is mostly tested on simulated data with known parameters. Here…

This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…

We consider the problem of the uniform (in $L_\infty$) recovery of ridge functions $f(x)=\varphi(\langle a,x\rangle)$, $x\in B_2^n$, using noisy evaluations $y_1\approx f(x^1),\ldots,y_N\approx f(x^N)$. It is known that for classes of…

We consider the {\it noisy polynomial interpolation problem\/} of recovering an unknown $s$-sparse polynomial $f(X)$ over the ring $\mathbb Z_{p^k}$ of residues modulo $p^k$, where $p$ is a small prime and $k$ is a large integer parameter,…

In practice most functional data cannot be recorded on a continuum, but rather at discrete time points. It is also quite common that these measurements come with an additive error, which one would like eliminate for the statistical…

In this note, we analyze an iterative soft / hard thresholding algorithm with homotopy continuation for recovering a sparse signal $x^\dag$ from noisy data of a noise level $\epsilon$. Under suitable regularity and sparsity conditions, we…

This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is…

We introduce a Prony-like method to recover a continuous domain 2-D piecewise smooth image from few of its Fourier samples. Assuming the discontinuity set of the image is localized to the zero level-set of a trigonometric polynomial, we…

This paper discusses the noisy phase retrieval problem: recovering a complex image signal with independent noise from quadratic measurements. Inspired by the dark fringes shown in the measured images of the array detector, a novel phase…

We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of…

In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…

We consider the problem of recovering spatially resolved polarization information from receiver Jones matrices. We introduce a physics-based learning approach, improving noise resilience compared to previous inverse scattering methods,…