Related papers: Adaptive Optimal Signal (Cardiogram) Processing, w…
A parameter estimation problem is considered for a linear stochastic hyperbolic equation driven by additive space-time Gaussian white noise. The damping/amplification operator is allowed to be unbounded. The estimator is of spectral type…
We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…
We summarize the theory of coronagraphic optics, and identify a dimensionless fine-tuning parameter, F, which we use to describe the Lyot stop size in the natural units of the coronagraphic optical train and the observing wavelength. We…
In this paper we consider functions in the Hardy space $\mathbf{H}_2^{p\times q}$ defined in the unit disc of matrix-valued. We show that it is possible, as in the scalar case, to decompose those functions as linear combinations of suitably…
We construct an adaptive asymptotically optimal in order in the $ L(2) $ sense a solution (estimation) of an integral linear equation of a first kind and energy of this solution with the confidence region building, also adaptive.
The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…
We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found.…
Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
Radio interferometers observe the Fourier space of the sky, at locations determined by the array geometry. Before a real space image is constructed by a Fourier transform, the data is weighted to improve the quality of reconstruction. Two…
For some Poisson-type model problem, we prove that adaptive FEM driven by the (h-h/2)-type error estimators from [Ferraz-Leite, Ortner, Praetorius, Numer. Math. 116 (2010)] leads to convergence with optimal algebraic convergence rates.…
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a…
In this paper, we establish optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal processing, image processing, and computer vision, among…
We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test…
This paper examines the problem of estimating the parameters of a bandlimited signal from samples corrupted by random jitter (timing noise) and additive iid Gaussian noise, where the signal lies in the span of a finite basis. For the…
Practical systems often suffer from hardware impairments that already appear during signal generation. Despite the limiting effect of such input-noise impairments on signal processing systems, they are routinely ignored in the literature.…
This paper aims to derive explicit and computable error bounds for the asymptotic expansion of the Jacobi polynomials as their degree approaches infinity, using an integral method. The analysis focuses on the outer or oscillatory region of…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…