相关论文: Compressive sampling with chaotic dynamical system…
Wide-area data and algorithms in large power systems are creating new opportunities for implementation of measurement-based dynamic load modeling techniques. These techniques improve the accuracy of dynamic load models, which are an…
We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…
The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number…
Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…
The problem of recovering a structured signal $\mathbf{x} \in \mathbb{C}^p$ from a set of dimensionality-reduced linear measurements $\mathbf{b} = \mathbf {A}\mathbf {x}$ arises in a variety of applications, such as medical imaging,…
Radar imaging systems transmit modulated wideband waveform to achieve high range resolution resulting in high sampling rates at the receiver proportional to the bandwidth of the transmit waveform. Analog processing techniques can be used on…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal…
The recently introduced theory of compressive sensing (CS) enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be…
The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing,…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications,…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…