arXiv subjects

Milos Dakovic

Publications and source records attributed to Milos Dakovic.

22 records · Page 2Linked to original sources

arXiv2015

Compressive Sensing of Sparse Signals in the Hermite Transform Basis: Analysis and Algorithm for Signal Reconstruction

An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the probability of success in detection of signal components support is determined. Based on the probabilistic analysis, a threshold for the detection of signal components is provided. It is a crucial step in the definition of a simple non-iterative algorithm for compressive sensing signal reconstruction. The derived theoretical concepts are proved on several examples using different statistical tests.

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arXiv2015

Reconstruction of Randomly Sampled Sparse Signals Using an Adaptive Gradient Algorithm

Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the remaining missing samples/measurements is recently proposed. The available samples are fixed, while the missing samples are considered as minimization variables. Recovery of missing samples/measurements is done using an adaptive gradient-based algorithm in the time domain. A new criterion for the parameter adaptation in this algorithm, based on the gradient direction angles, is proposed. It improves the algorithm computational efficiency. A theorem for the uniqueness of the recovered signal for given set of missing samples (reconstruction variables) is presented. The case when available samples are a random subset of a uniformly or nonuniformly sampled signal is considered in this paper. A recalculation procedure is used to reconstruct the nonuniformly sampled signal. The methods are illustrated on statistical examples.

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arXiv2015

Hardware Architecture for Single Iteration Reconstruction Algorithm

A hardware architecture for the single iteration algorithm is proposed in this paper. Single iteration algorithm enables reconstruction of the full signal when small number of signal samples is available. The algorithm is based on the threshold calculation, and allows distinguishing between signal components and noise that appears as a consequence of missing samples. The proposed system for hardware realization is divided into three parts, each part with different functionality. The system is suitable for the FPGA realization. Realization of the blocks for which there are no standard components in FPGA, is discussed as well.

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arXiv2013

Adaptive Variable Step Algorithm for Missing Samples Recovery in Sparse Signals

Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as compressive sensed signals by omitting the corrupted samples and considering them as unavailable during the recovery process. The reconstruction of missing samples is done by using one of the well known reconstruction algorithms. In this paper we will propose a very simple and efficient adaptive variable step algorithm, applied directly to the concentration measures, without reformulating the reconstruction problem within the standard linear programming form. Direct application of the gradient approach to the nondifferentiable forms of measures lead us to introduce a variable step size algorithm. A criterion for changing adaptive algorithm parameters is presented. The results are illustrated on the examples with sparse signals, including approximately sparse signals and noisy sparse signals.

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