Motion estimation using higher-order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimating motion even for small regions or blocks. Using higher than second-order statistics is appropriate in case the image sequence is severely corrupted by additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.Peer Reviewe

Radon spectrogram-based approach for automatic IFs separation

The separation of overlapping components is a well-known and difficult problem in multicomponent signals analysis and it is shared by applications dealing with radar, biosonar, seismic, and audio signals. In order to estimate the instantaneous frequencies of a multicomponent signal, it is necessary to disentangle signal modes in a proper domain. Unfortunately, if signal modes supports overlap both in time and frequency, separation is only possible through a parametric approach whenever the signal class is a priori fixed. In this work, time-frequency analysis and Radon transform are jointly used for the unsupervised separation of modes of a generic frequency modulated signal in noisy environment. The proposed method takes advantage of the ability of the Radon transform of a proper time-frequency distribution in separating overlapping modes. It consists of a blind segmentation of signal components in Radon domain by means of a near-to-optimal threshold operation. The inversion of the Radon transform on each detected region allows us to isolate the instantaneous frequency curves of each single mode in the time-frequency domain. Experimental results performed on constant amplitudes chirp signals confirm the effectiveness of the proposed method, opening the way for its extension to more complex frequency modulated signals

Linear and synchrosqueezed time–frequency representations revisited:overview, standards of use, resolution, reconstruction, concentration, and algorithms

Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review of these TFRs, summarizing all practically relevant aspects of their use, reconsidering some conventions and introducing new concepts and procedures to advance their applicability and value. Furthermore, a detailed numerical and theoretical study of three specific questions is provided, relevant to the application of these methods, namely: the effects of the window/wavelet parameters on the resultant TFR; the relative performance of different approaches for estimating parameters of the components present in the signal from its TFR; and the advantages/drawbacks of synchrosqueezing. In particular, we show that the higher concentration of the synchrosqueezed transforms does not seem to imply better resolution properties, so that the SWFT and SWT do not appear to provide any significant advantages over the original WFT and WT apart from a more visually appealing pictures. The algorithms and Matlab codes used in this work, e.g. those for calculating (S)WFT and (S)WT, are freely available for download

Nonparametric Detection and Estimation of Highly Oscillatory Signals

This thesis considers the problem of detecting and estimating highly oscillatory signals from noisy measurements. These signals are often referred to as chirps in the literature; they are found everywhere in nature, and frequently arise in scientific and engineering problems. Mathematically, they can be written in the general form A(t) exp(ilambda varphi(t)), where lambda is a large constant base frequency, the phase varphi(t) is time-varying, and the envelope A(t) is slowly varying. Given a sequence of noisy measurements, we study two problems seperately: 1) the problem of testing whether or not there is a chirp hidden in the noisy data, and 2) the problem of estimating this chirp from the data. This thesis introduces novel, flexible and practical strategies for addressing these important nonparametric statistical problems. The main idea is to calculate correlations of the data with a rich family of local templates in a first step, the multiscale chirplets, and in a second step, search for meaningful aggregations or chains of chirplets which provide a good global fit to the data. From a physical viewpoint, these chains correspond to realistic signals since they model arbitrary chirps. From an algorithmic viewpoint, these chains are identified as paths in a convenient graph. The key point is that this important underlying graph structure allows to unleash very effective algorithms such as network flow algorithms for finding those chains which optimize a near optimal trade-off between goodness of fit and complexity. Our estimation procedures provide provably near optimal performance over a wide range of chirps and numerical experiments show that both our detection and estimation procedures perform exceptionally well over a broad class of chirps. This thesis also introduces general strategies for extracting signals of unknown duration in long streams of data when we have no idea where these signals may be. The approach is leveraging testing methods designed to detect the presence of signals with known time support. Underlying our methods is a general abstraction which postulates an abstract statistical problem of detecting paths in graphs which have random variables attached to their vertices. The formulation of this problem was inspired by our chirp detection methods and is of great independent interest.</p

Оптимальный алгоритм оценивания координатно-информативных параметров MSK-сигналов пакетных радиосетей с неизвестным законом первичной модуляции на основе нелинейной чирплет-аппроксимации

New results on the recently introduced signal processing methods based on matching pursuit and modified nonlinear chirplet approximation are presented. The optimal estimation algorithm for time of arrival of MSK radio signals of packet radio in area distributed receiving points of range difference position location system is developed. The comparison of developed algorithm with known is performed.Предложен научно-методический аппарат обработки радиосигналов на основе поиска совпадений и модифицированной нелинейной чирплет-аппроксимации. Разработан оптимальный алгоритм оценивания времени прихода MSK-радиосигналов пакетных радиосетей в пространственно-разнесенных пунктах приема разностно-дальномерной системы местоопределения. Произведено сравнение разработанного алгоритма с известными

Extraction of instantaneous frequencies for signals with intersecting and intermittent trajectories

A multicomponent signal usually presents multiple trajectories with time-varying frequencies and amplitudes in a time–frequency distribution (TFD). One can extract the ridges corresponding to true signal components and then reconstruct them to recover signal signatures. Most current practices for ridge extraction assume that each trajectory runs throughout the entire time axis without cross-terms. However, this hypothesis is inconsistent with the truth of many measured signals. The increasing application occasions require further consideration of complicated intersecting and intermittent cases. This study addresses this issue and proposes a novel intersecting and intermittent trajectory tracking (IITT) approach. We first develop a data-driven method to effectively isolate peaks from noises in a TFD and generate a dependable peak spectrum. Then, we propose a dynamic optimization tracking function to decide upon the acceptance of the peaks corresponding to an individual component based on the purified spectrum. The IITT approach fully exploits the information from the raw signal without any prior knowledge while promising robustness to the variations of ridge numbers, ridges’ births and deaths, and its continuation and discontinuation. Two simulated and three measured signals are utilized to assess the performance of the proposed IITT. The success elements of the IITT are revealed and discussed in detail at the end of the paper