Srdjan Stankovic

Watermarking in the space/spatial-frequency domain using two-dimensional Radon-Wigner distribution

A two-dimensional (2-D) signal with a variable spatial frequency is proposed as a watermark in the spatial domain. This watermark is characterized by a linear frequency change. It can be efficiently detected by using 2-D space/spatial-frequency distributions. The projections of the 2-D Wigner distribution--the 2-D Radon-Wigner distribution, are used in order to emphasize the watermark detection process. The watermark robustness with respect to some very important image processing attacks, such as for example, the translation, rotation, cropping, JPEG compression, and filtering, is demonstrated and tested by using Stirmark 3.1.

Digital watermarking in the fractional Fourier transformation domain

An application of the fractional Fourier transform for the multimedia copyright protection is proposed in the paper. The watermark robustness as well as statistical performance are considered.

Separation of target rigid body and micro-doppler effects in ISAR imaging

Micro-Doppler (m-D) effect is caused by moving parts of the radar target. It can cover rigid parts of a target and degrade the inverse synthetic aperture radar (ISAR) image. Separation of the patterns caused by stationary parts of the target from those caused by moving (rotating or vibrating) parts is the topic of this paper. Two techniques for separation of the rigid part from the rotating parts have been proposed. The first technique is based on time-frequency (TF) representation with sliding window and order statistics techniques. The first step in this technique is recognition of rigid parts in the range/cross-range plane. In the second step, reviewed TF representation and order statistics setup are employed to obtain signals caused by moving parts. The second technique can be applied in the case of very emphatic m-D effect. In the first step the rotating parts are recognized, based on the inverse Radon transform (RT). After masking these patterns, a radar image with the rigid body reflection can be obtained. The proposed methods are illustrated by examples

Fast communication: Missing samples analysis in signals for applications to L-estimation and compressive sensing

This paper provides statistical analysis for efficient detection of signal components when missing data samples are present. This analysis is important for both the areas of L-statistics and compressive sensing. In both cases, few samples are available due to either noisy sample elimination or random undersampling signal strategies. The analysis enables the determination of the sufficient number of observation and as such the minimum number of missing samples which still allow proper signal detection. Both single component and multicomponent signals are considered. The results are verified by computer simulations using different component frequencies and under various missing-available samples scenarios.

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.

Local polynomial Fourier transform: A review on recent developments and applications

The local polynomial Fourier transform (LPFT), as a high-order generalization of the short-time Fourier transform (STFT), has been developed and used for many different applications in recent years. This paper attempts to review previous research work on the following issues of the LPFT. Firstly, the definition, the properties of the LPFT and its relationships with other transforms are reviewed. The LPFT for multicomponent signal is then presented. The polynomial time frequency transform (PTFT), which is the maximum likelihood estimator to estimate the parameters in the LPFT, as well as its properties and fast algorithms are discussed. By comparing with the Fourier transform (FT), the STFT and the Wigner-Ville distribution (WVD), the LPFT has its superiority in obtaining improved SNRs, which can be supported by theoretical analysis and computer simulations. Furthermore, the reassignment method is combined with the LPFT and the robust LPFT to improve the concentration of the signal representation in the time-frequency domain. Performances obtained by using various LPP-related methods are compared for signals in different noise environments, such as the additive white Gaussian noise (AGWN), impulsive noise, and the mixture of AGWN and impulsive noise.

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 architecture for the realization of a system for time-frequency signal analysis

An architecture of the system for time-frequency signal analysis is presented. This system is based on the S-method, whose special cases are two the most important distributions: the spectrogram and the Wigner distribution. Systems with constant and signal-dependent window widths are presented.