Milos Brajovic

On the parameterization of Hermite transform with application to the compression of QRS complexes

The concentration and sparsity of signal representation in the Hermite transform (HT) basis may highly depend on a properly chosen scaling factor and discrete time shift parameter. In that sense, we propose a simple and efficient iterative procedure for automatic determination of the optimal scaling factor. The optimization criterion is based on the ź1-norm acting as a measure of signal concentration in the HT domain. Instead of centering the signal at the zero time instant, we also propose to shift the center for a few points left or right, which will additionally improve the concentration. An important application of the proposed optimization approach is the compression of QRS complexes, where properly chosen scaling factor and time-shift increase the compression performance. The results are verified using synthetic and real examples and compared with the existing approach for the compression of QRS complexes. The algorithm for optimization of scaling factor and time-shift of Hermite functions is proposed.Parameters are optimized to provide the most concentrated representation of the observed signals.The simple iterative algorithm is based on gradient descent method.The concentration measure is employed as optimization criterion.The efficiency of the proposed approach is verified using both real and synthetic signals.The method is applied for QRS compression and tested on a database of QRS complexes.The efficiency is proven also for T waves of ECG signals and UWB signals.

An algorithm for micro-Doppler period estimation

Radar micro-Doppler signatures are important in identification of properties of unknown targets. Many applications in real world scenarios require estimation of micro-Doppler parameters. Micro-Doppler oscillation period is one of its important parameters. A new algorithm for micro-Doppler oscillation period estimation based on time frequency signal analysis is proposed. Its functionality and theoretical considerations are evaluated using synthetic data, and numerical results are presented.

Time-frequency decomposition of multivariate multicomponent signals

Abstract A solution of the notoriously difficult problem of characterization and decomposition of multicomponent multivariate signals which partially overlap in the joint time-frequency domain is presented. This is achieved based on the eigenvectors of the signal autocorrelation matrix. The analysis shows that the multivariate signal components can be obtained as linear combinations of the eigenvectors that minimize the concentration measure in the time-frequency domain. A gradient-based iterative algorithm is used in the minimization process and for rigor, a particular emphasis is given to dealing with local minima associated with the gradient descent approach. Simulation results over illustrative case studies validate the proposed algorithm in the decomposition of multicomponent multivariate signals which overlap in the time-frequency domain.

Convexity of the ℓ1-norm based sparsity measure with respect to the missing samples as variables

Sparse signal processing and the reconstruction of missing samples of signals exhibiting sparsity in a transform domain have been emerging research topics during the last decade. In this paper, we present the proof of the sparsity measure convexity, when considering the missing samples as minimization variables. The sparsity measure can be directly exploited in the reconstruction procedures, such as in the recently proposed gradient-based reconstruction algorithm. It makes the proof of sparsity measure convexity with respect to the missing samples as minimization variables especially interesting for signal processing. The minimal value of the sparsity measure corresponds to the set of missing sample values representing the sparsest possible solution, assuming that the reconstruction conditions are met. Convexity, along with recently presented proof of the uniqueness of the acquired solution, makes the gradient-based algorithm with missing samples as variables, a complete approach to the signal reconstruction. If the sparsity measure is convex, then we can guarantee that the solution corresponds to the global minimum of the sparsity measure, since the local minima do not exist in that case.

The Optimization of the Hermite transform: Application perspectives and 2D generalization

This paper studies the discrete Hermite transform applicability in concise representation of short-term and windowed sinusoidal signals. Namely, the Hermite functions show similar behavior with windowed multi-tone signals and filtered tones, which opens the possibility for signal sparsifation using an optimal transform scaling factor. In other words, the scaling factor is optimized in order to enhance the transform coefficients concentration. The scaling factor optimization method is based on concentration measures and it is further generalized to the case of 2D Hermite transform. Numerical examples illustrate the presented theoretical framework.

FHSS signal sparsification in the Hermite transform domain

Signal sparsity is exploited in various signal processing approaches. The applicability ranges from compression, signal classification, coding, etc. Finding a suitable basis where the signal exhibits a compact (sparse) support is a challenging task and the result mainly depends on the signal nature. In this paper, we observed sinusoidally modulated signals appearing in wireless communications, namely the FHSS signals. As a sparsity domain, the Hermite transform domain is considered. The Hermite basis functions resemble the shapes of the FHSS signal components, and therefore these are considered as suitable for compact representation. In order to improve the sparsity of the observed signal components, we propose to employ a procedure for the Hermite transform optimization. As a result, the discrete Hermite functions better fit the signal components, producing just negligible errors between the original and optimized signal. The theory is verified by the experimental results. The procedure is tested on synthetic FHSS signal.

The analysis of missing samples in signals sparse in the hermite transform domain

The influence of missing samples in signals which exhibit sparsity in the domain of Hermite transform is analyzed. The study provides theoretical concepts for the efficient reconstruction of the signals with missing samples. Single component signals are analyzed, and the main results guarantee further generalization of the presented concepts to the case of multicomponent signals. The theoretical contributions are confirmed through several numerical examples.

Instantaneous frequency estimation using Ant colony optimization and Wigner distribution

Instantaneous frequency estimation of signals in a high noise environment is analyzed in the paper. An algorithm based on Ant colony optimization and Wigner distribution is proposed for solving the considered estimation problem. The proposed approach has been applied and tested on mono-component frequency-modulated signals. Numerical examples are given in order to demonstrate the algorithms performances in the analyzed framework.

Error in the Reconstruction of Nonsparse Images

Sparse signals, assuming a small number of nonzero coefficients in a transformation domain, can be reconstructed from a reduced set of measurements. In practical applications, signals are only approximately sparse. Images are a representative example of such approximately sparse signals in the two-dimensional (2D) discrete cosine transform (DCT) domain. Although a significant amount of image energy is well concentrated in a small number of transform coefficients, other nonzero coefficients appearing in the 2D-DCT domain make the images be only approximately sparse or nonsparse. In the compressive sensing theory, strict sparsity should be assumed. It means that the reconstruction algorithms will not be able to recover small valued coefficients (above the assumed sparsity) of nonsparse signals. In the literature, this kind of reconstruction error is described by appropriate error bound relations. In this paper, an exact relation for the expected reconstruction error is derived and presented in the form of a theorem. In addition to the theoretical proof, the presented theory is validated through numerical simulations.

Analysis of the Reconstruction of Sparse Signals in the DCT Domain Applied to Audio Signals

Sparse signals can be reconstructed from a reduced set of signal samples using compressive sensing (CS) methods. The discrete cosine transform (DCT) can provide highly concentrated representations of audio signals. This property implies the DCT as a good sparsity domain for the audio signals. In this paper, the DCT is studied within the context of sparse audio signal processing using the CS theory and methods. The DCT coefficients of a sparse signal, calculated with a reduced set of available samples, can be modeled as random variables. It has been shown that the statistical properties of these variables are closely related to the unique reconstruction conditions. The main result of this paper is in an exact formula for the mean-square reconstruction error in the case of approximately sparse and nonsparse noisy signals reconstructed under the sparsity assumption. Based on the presented analysis, a simple and computationally efficient reconstruction algorithm is proposed. The presented theoretical concepts and the efficiency of the reconstruction algorithm are verified numerically, including examples with synthetic and recorded audio signals with unavailable or corrupted samples. Random disturbances and disturbances simulating clicks or inpainting in audio signals are considered. Statistical verification is done on a dataset with experimental signals. Results are compared with some classical and recent methods used in similar signal and disturbance scenarios.