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The nonlinear spline adaptive filtering under least mean square (SAF-LMS) uses the mean square error (MSE) based cost function to identify the Wiener-type nonlinear systems, which is rational under the assumption of Gaussian distributions. However, the mere second-order statistics are often not suitable for nonlinear and/or non-Gaussian systems. To address this issue, a new nonlinear adaptive filter,...
In this paper, we develop parallel algorithms for a family of regularized multi-task methods which can model task relations under the regularization framework. Since those multi-task methods cannot be parallelized directly, we use the FISTA algorithm, which in each iteration constructs a surrogate function of the original problem by utilizing the Lipschitz structure of the objective function based...
In this paper, we study how to initialize the convolutional neural network (CNN) model for training on a small dataset. Specially, we try to extract discriminative filters from the pre-trained model for a target task. On the basis of relative entropy and linear reconstruction, two methods, Minimum Entropy Loss (MEL) and Minimum Reconstruction Error (MRE), are proposed. The CNN models initialized by...
With regard to ground-based astronomy observations, due to the interference of atmospheric turbulence, noise and other factors, the observed images are degraded, which makes it difficult to obtain high-resolution astronomical images. In such case, astronomical image restoration is essential. Of all the image deconvolution algorithms, the one based on scaled gradient projection (SGP) is highly effective...
This paper considers the regularized learning schemes based on ℓ1-regularizer and the ε-insensitive pinball loss in a data dependent hypothesis space. The target is the error analysis for the conditional quantile regression learning. Except for continuity and boundedness, the kernel function is not necessary to satisfy any further regularity conditions. The data dependent nature of the algorithm leads...
A simple iterative algorithm is presented for the calculation of the electromagnetic radiation scattered from objects of arbitrary shape made from either lossless or lossy dielectrics or conductors. Convergence of the algorithm is tested on materials of all such types. It is found that the algorithm converges for all materials; faster for lossy ones.
A numerical study of the scattering of an acoustic plane wave by an infinite cylindrical structure with corners is reported. An integral equation formulation is employed for which rapidly convergent quadrature schemes are developed. Three different boundary conditions are examined - Dirichlet, Neumann and an impedance condition. The effect on the scattered field of rounding the corners is measured...
We present a theoretical comparison of the state-of-the-art sufficient conditions required for pathwise (almost sure type of) convergence between grid based and particle approximate filters, as well as discuss the implications of these conditions on the specific mode of convergence achieved. Focusing on general Markov processes observed in conditionally Gaussian noise, we have recently shown that...
In this paper, we will propose a new framework which can estimate the desired signal and the instrument response function (IRF) simultaneously from the degraded spectral signal. Firstly, the spectral signal is considered as a distribution, thus, new entropy (called differential-entropy, DE) is defined to measure the distribution with a uniform distribution, which allows negative value existing. Moreover,...
In this paper, we propose a novel structure for implementing a kernel adaptive filter as an add-on component for a linear adaptive filter. The kernel adaptive filter has been proposed as a solution to non-linear adaptive problems and their effectiveness has been demonstrated. However, it is not intended for replacing the linear adaptive filters at all, rather, we expect it to complement the performance...
Adaptive channel equalisation is a signal processing technique to mitigate inter-symbol interference (ISI) in a time dispersive channel. To this end, the use of least mean squares (LMS) algorithm and its variants is widespread since they minimise the minimum mean squared error (MMSE) criteria by online stochastic gradient algorithms and they asymptotically tend to the optimal Weiner solution for linearly...
This paper presents a new approach to statistically characterize the variability of intermodulation distortion of nonlinear RF circuits in response to uncertainty in the design parameters. The proposed approach is built upon two ideas. The first idea is a moment-based computation of the Volterra Kernels. The second idea is derived from the recently reported decoupled formulation of the Hermite-based...
Convolutional Neural Network (CNN) is a type of feed-forward artificial neural network, exploiting the unknown structure in input distribution to discover good representations with multiple layers of small neuron collections. CNN uses relatively little pre-processing compared to other classification algorithms, usually uses gradient decent to updates the parameters in the network. Since CNN was introduced...
This paper provides a method for the L1 analysis of sampled-data systems, by which we mean the computation of their L∞-induced norm. We first apply the lifting approach to sampled-data systems and derive an operator theoretic representation of their input/output relation. We then apply fast-lifting by which the sampling interval [0, h) is divided into M subintervals with an equal width, and provide...
Unlike traditional methods that aim to approximate a function over a large compact set, a function approximation method is developed in this paper that aims to approximate a function in a small neighborhood of a state that travels within a compact set. The development is based on universal reproducing kernel Hilbert spaces over the n..dimensional Euclidean space. Three theorems are introduced that...
The normalized least mean pth power (NLMP) algorithm based on adaptive Volterra filters has conflicting requirement of fast convergence rate and low steady-state error. To address this problem, a novel combination of two NLMP (CNLMP) algorithms is proposed which adaptively combines two independent NLMP filters with large and small step sizes to obtain fast convergence rate and low misadjustment in...
The paper deals with the design of a state observer for linear time-invariant systems, which converges in finite-time without resorting to high-gain injection. The devised observer is based on modulation integrals as the main enabling tool, and can be implemented as a jump-linear system. The dynamics of the state estimation error is proven to be input-to-state stable with respect to the additive measurement...
The main aim of this paper is to study some boundedness inequalities of certain semi-discrete operators. These operators allow to unify some inequalities for both the Shannon sampling operators and Kantorovich-type operators.
We survey recent results in the subject of interpolating bandlimited functions from their samples at both uniform and nonuniform sets via translates of a family of multiquadrics. Recovery of the original function is considered by means of a limiting process which changes a shape parameter associated with the multiquadric function. We also discuss some ways in which approximation rates can be found...
We study the identification problem for linear time-variant communication channels on the circle, extending earlier work on the real line. We therefore resolve a suitably formulated periodic version of the conjectures of Kailath and Bello regarding channel identification.
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