Irena Orovic

Compressive Sensing Based Separation of Nonstationary and Stationary Signals Overlapping in Time-Frequency

A compressive sensing (CS) approach for nonstationary signal separation is proposed. This approach is motivated by challenges in radar signal processing, including separations of micro-Doppler and main body signatures. We consider the case where the signal of interest assumes sparse representation over a given basis. Other signals present in the data overlap with the desired signal in the time and frequency domains, disallowing conventional windowing or filtering operations to be used for desired signal recovery. The proposed approach uses linear time-frequency representations to reveal the data local behavior. Using the L-statistics, only the time-frequency (TF) points that belong to the desired signal are retained, whereas the common points and others pertaining only to the undesired signals are deemed inappropriate and cast as missing samples. These samples amount to reduced frequency observations in the TF domain. The linear relationship between the measurement and sparse domains permits the application of CS techniques to recover the desired signal without significant distortion. We focus on sinusoidal desired signals with sparse frequency-domain representation but show that the analysis can be straightforwardly generalized to nonsinusoidal signals with known structures. Several examples are provided to demonstrate the effectiveness of the proposed approach.

Fast communication: An automated signal reconstruction method based on analysis of compressive sensed signals in noisy environment

An analysis of signal reconstruction possibility using a small set of samples corrupted by noise is considered. False detection and/or misdetection of sparse signal components may occur as a twofold influence of noise: one is a consequence of missing samples, while the other appears from an external source. This analysis allows us to determine a minimal number of available samples required for a non-iterative reconstruction. Namely, using a predefined probability of error, it is possible to define a general threshold that separates signal components from spectral noise. In the cases when some components are masked by noise, this threshold can be iteratively updated. It will render that all components are detected, providing an iterative version of blind and simple compressive sensing reconstruction algorithm.

A new approach for classification of human gait based on time-frequency feature representations

We introduce a new and simple technique for human gait classification based on the time-frequency analysis of radar data. The focus is on the classification of arm movements to discern free vs. confined arm swinging motion. The latter may arise in hostage situation or may be indicative to carrying objects with one or both hands. The motion signatures corresponding to the arm and leg movements are both extracted from the time-frequency representation of the micro-Doppler. The time-frequency analysis is performed using the multiwindow S-method. With the Hermite functions acting as multiwindows, it is shown that the Hermite S-method provides an efficient representation of the complex Doppler associated with human walking. The proposed human gait classification technique utilizes the arm positive and negative Doppler frequencies and their relative time of occurrence. It is tested on various real radar signals and shown to provide an accurate classification.

Robust Time-Frequency Analysis Based on the L-Estimation and Compressive Sensing

The L-estimate transforms and time-frequency representations are presented within the framework of compressive sensing. The goal is to recover signal or local auto-correlation function samples corrupted by impulse noise. The signal is assumed to be sparse in a transform domain or in a joint-variable representation. Unlike the standard L-statistics approach, which suffers from degraded spectral characteristics due to the omission of samples, the compressive sensing in combination with the L-estimate permits signal reconstruction that closely approximates the noise free signal representation.

An Application of Multidimensional Time-Frequency Analysis as a Base for the Unified Watermarking Approach

A watermarking approach based on multidimensional time-frequency analysis is proposed. It represents a unified concept that can be used for different types of data such as audio, speech signals, images or video. Time-frequency analysis is employed for speech signals, while space/spatial-frequency analysis is used for images. Their combination is applied for video signals. Particularly, we focus on the 2-D case: space/spatial-frequency based image watermarking procedure that will be subsequently extended to video signal. A method that selects coefficients for watermarking by estimating the local frequency content is proposed. In order to provide watermark imperceptibility, the nonstationary filtering is used to model the watermark which corresponds to the host signal components. Furthermore, the watermark detection within the multidimensional time-frequency domain is proposed. The efficiency and robustness of the procedure in the presence of various attacks is proven experimentally.

A Virtual Instrument for Time-Frequency Analysis of Signals With Highly Nonstationary Instantaneous Frequency

This paper presents an open-source virtual instrument for time-frequency analysis. The purpose is to show the correct practical implementation, and the performance, of a number of complex algorithms and of a practical criterion (the concentration measure) to select the proper algorithm for a given signal. The virtual instrument provides efficient solutions for signals with a highly nonstationary instantaneous frequency. Despite variations of signal phase function, a high concentration can be achieved by a suitable choice of distribution form. The distribution can be chosen manually, or the instrument can perform optimal distribution selection. Namely, a procedure for the automated selection of optimal distribution order is provided. The concentration measure is employed as a selection criterion. A variety of options provides different comparisons for several distributions simultaneously. Efficiency of the proposed instrument is demonstrated on various examples. It is important to emphasize that an extensive and complex theory is implemented as a set of open-source algorithms. All the algorithms can be used “as is” or modified and upgraded (even separately) by researchers and practitioners in the field. The virtual instrument is available at http://www.tfsa.ac.me/Open_source_codes.html,, or upon request to the authors.

Relationship between the robust statistics theory and sparse compressive sensed signals reconstruction

An analysis of robust estimation theory in the light of sparse signals reconstruction is considered. This approach is motivated by compressive sensing (CS) concept which aims to recover a complete signal from its randomly chosen, small set of samples. In order to recover missing samples, the authors define a new reconstruction algorithm. It is based on the property that the sum of generalised deviations of estimation errors, obtained from robust transform formulations, has different behaviour at signal and non-signal frequencies. Additionally, this algorithm establishes a connection between the robust estimation theory and CS. The effectiveness of the proposed approach is demonstrated on examples.

Fast communication: L-statistics based modification of reconstruction algorithms for compressive sensing in the presence of impulse noise

A modification of standard compressive sensing algorithms for sparse signal reconstruction in the presence of impulse noise is proposed. The robust solution is based on the L-estimate statistics which is used to provide appropriate initial conditions that lead to improved performance and efficient convergence of the reconstruction algorithms.

Effects of Cauchy Integral Formula Discretization on the Precision of IF Estimation: Unified Approach to Complex-Lag Distribution and its Counterpart L-Form

Effects of Cauchy integral formula discretization on the concentration of time-frequency (TF) distribution are analyzed. As a result of this discretization, new forms of distributions are produced. In order to increase the accuracy of instantaneous frequency (IF) estimation, two solutions are considered: increasing the number of integration points and multiple successive integrations using the same number of points (it corresponds to the L-form of the TF distribution). In practical applications, the L-form of the fourth-order complex-lag distribution produces very efficient representation. In this case, the analysis of noise influence is also provided.

Time-frequency-based instantaneous frequency estimation of sparse signals from incomplete set of samples

The estimation of time-varying instantaneous frequency (IF) for monocomponent signals with an incomplete set of samples is considered. A suitable time-frequency distribution (TFD) reduces the non-stationary signal into a local sinusoid over the lag variable prior to the Fourier transform. Accordingly, the observed spectral content becomes sparse and suitable for compressive sensing reconstruction in the case of missing samples. Although the local bilinear or higher order auto-correlation functions will increase the number of the missing samples, the analysis shows that an accurate IF estimation can be achieved even if we deal with only few samples, as long as the auto-correlation function is properly chosen to coincide with the signals phase non-linearity. In addition, by employing the sparse signal reconstruction algorithms, ideal time-frequency representations are obtained. The presented theory is illustrated on several examples dealing with different auto-correlation functions and corresponding TFDs.