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

Motivated by a recently introduced HIMMO key distribution scheme, we consider a modification of the noisy polynomial interpolation problem of recovering an unknown polynomial $f(X) \in Z[X]$ from approximate values of the residues of $f(t)$…

In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a $K$-sparse complex signal $s \in \mathbb{C}^n$, from a set of $m$ noisy quadratic…

Imitation learning (IL) aims to learn a policy from expert demonstrations and has been applied to various applications. By learning from the expert policy, IL methods do not require environmental interactions or reward signals. However,…

Representing 3D objects and scenes with neural radiance fields has become very popular over the last years. Recently, surface-based representations have been proposed, that allow to reconstruct 3D objects from simple photographs. However,…

In this paper, we study the nonlinear inverse problem of estimating the spectrum of a system matrix, that drives a finite-dimensional affine dynamical system, from partial observations of a single trajectory data. In the noiseless case, we…

In the noisy population recovery problem of Dvir et al., the goal is to learn an unknown distribution $f$ on binary strings of length $n$ from noisy samples. For some parameter $\mu \in [0,1]$, a noisy sample is generated by flipping each…

We introduce a new numerical algorithm for solving the stochastic neural field equation (NFE) with delays. Using this algorithm we have obtained some numerical results which illustrate the effect of noise in the dynamical behaviour of…

This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…

This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…

The paper concerns problems of the recovery of operators from noisy information in weighted $L_q$-spaces with homogeneous weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson…

We present an algorithm based on numerical techniques that have become standard for solving nonlinear integral equations: Newton's method, homotopy continuation, the multilevel method and random projection to solve the inversion problem…

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…

The main objective of this paper is to find algorithms accompanied by explicit error bounds for phase retrieval from noisy magnitudes of frame coefficients when the underlying frame has a low redundancy. We achieve these goals with frames…

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…

Bessel functions with pure imaginary index (order) play an important role in corpuscular optics where they govern the dynamics of charged particles in isotrajectory quadrupoles. Recently they were found to be of great importance in…

This paper deals with impulse noise removal from color images. The proposed noise removal algorithm employs a novel approach with morphological filtering for color image denoising; that is, detection of corrupted pixels and removal of the…

In this paper, we propose a novel estimator of the instantaneous frequencies (IFs) of the modes making up multicomponent signals (MCSs). We are particularly interested in dealing with noisy MCSs containing close modes in the time-frequency…

Many image processing applications benefited remarkably from the theory of sparsity. One model of sparsity is the cosparse analysis one. It was shown that using l_1-minimization one might stably recover a cosparse signal from a small set of…

The aim of noisy phase retrieval is to estimate a signal $\mathbf{x}_0\in \mathbb{C}^d$ from $m$ noisy intensity measurements $b_j=\left\lvert \langle \mathbf{a}_j,\mathbf{x}_0 \rangle \right\rvert^2+\eta_j, \; j=1,\ldots,m$, where…