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Antonio Cicone

Publications and source records attributed to Antonio Cicone.

30 records · Page 2Linked to original sources
arXiv2019

Study of boundary conditions in the Iterative Filtering method for the decomposition of nonstationary signals

Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal of decomposing such signals into simple oscillatory components. Several papers have been published regarding the analysis of this technique from a mathematical point of view. All these work start with the assumption that each compactly supported signal is extended outside the boundaries periodically. In this work we tackle the problem of studying the influence of different boundary conditions on the decompositions produce by the Iterative Filtering method.

math.NA↗
arXiv2018

Iterative Filtering as a direct method for the decomposition of non-stationary signals

The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to transform the Iterative Filtering method into a direct technique, making the algorithm closer to an online algorithm. We present a few numerical examples to show the effectiveness of the proposed approaches.

math.NA↗
arXiv2018

Numerical Analysis for Iterative Filtering with New Efficient Implementations Based on FFT

Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem of further analyzing the convergence of the Iterative Filtering method both in a continuous and a discrete setting in order to provide a comprehensive analysis of its behavior. Based on these results we provide new ideas for efficient implementations of Iterative Filtering algorithm which are based on Fast Fourier Transform (FFT), and the reduction of the original iterative algorithm to a direct method.

math.NA↗
arXiv2017

Nonstationary signal decomposition for dummies

How can I decompose a nonstationary signal? What are the advantages of using the most recent methods available in the literature versus using classical methods like (short time) Fourier transform or wavelet transform? This paper tries to address these and other questions providing the reader with a brief and self contained survey on what and how to tackle the decomposition of nonstationary signals.

math.HO↗
arXiv2017

How nonlinear-type time-frequency analysis can help in sensing instantaneous heart rate and instantaneous respiratory rate from photoplethysmography in a reliable way

Despite the population of the noninvasive, economic, comfortable, and easy-to-install photoplethysmography (PPG), it is still lacking a mathematically rigorous and stable algorithm which is able to simultaneously extract from a single-channel PPG signal the instantaneous heart rate (IHR) and the instantaneous respiratory rate (IRR). In this paper, a novel algorithm called deppG is provided to tackle this challenge. deppG is composed of two theoretically solid nonlinear-type time-frequency analyses techniques, the de-shape short time Fourier transform and the synchrosqueezing transform, which allows us to extract the instantaneous physiological information from the PPG signal in a reliable way. To test its performance, in addition to validating the algorithm by a simulated signal and discussing the meaning of "instantaneous", the algorithm is applied to two publicly available batch databases, the Capnobase and the ICASSP 2015 signal processing cup. The former contains PPG signals relative to spontaneous or controlled breathing in static patients, and the latter is made up of PPG signals collected from subjects doing intense physical activities. The accuracies of the estimated IHR and IRR are compared with the ones obtained by other methods, and represent the state-of-the-art in this field of research. The results suggest the potential of deppG to extract instantaneous physiological information from a signal acquired from widely available wearable devices, even when a subject carries out intense physical activities.

q-bio.NC↗
arXiv2016

Linear dynamical systems on graphs

We consider linear dynamical systems with a structure of a multigraph. The vertices are associated to linear spaces and the edges correspond to linear maps between those spaces. We analyse the asymptotic growth of trajectories (associated to paths along the multigraph), the stability and the stabilizability problems. This generalizes the classical linear switching systems and their recent extensions to Markovian systems, to systems generated by regular languages, etc. We show that an arbitrary system can be factorized into several irreducible systems on strongly connected multigraphs. For the latter systems, we prove the existence of invariant (Barabanov) multinorm and derive a method of its construction. The method works for a vast majority of systems and finds the joint spectral radius (Lyapunov exponent). Numerical examples are presented and applications to the study of fractals, attractors, and multistep methods for ODEs are discussed.

math.DS↗
arXiv2015

Hyperspectral Chemical Plume Detection Algorithms Based On Multidimensional Iterative Filtering Decomposition

Chemicals released in the air can be extremely dangerous for human beings and the environment. Hyperspectral images can be used to identify chemical plumes, however the task can be extremely challenging. Assuming we know a priori that some chemical plume, with a known frequency spectrum, has been photographed using a hyperspectral sensor, we can use standard techniques like the so called matched filter or adaptive cosine estimator, plus a properly chosen threshold value, to identify the position of the chemical plume. However, due to noise and sensors fault, the accurate identification of chemical pixels is not easy even in this apparently simple situation. In this paper we present a post-processing tool that, in a completely adaptive and data driven fashion, allows to improve the performance of any classification methods in identifying the boundaries of a plume. This is done using the Multidimensional Iterative Filtering (MIF) algorithm (arXiv:1411.6051, arXiv:1507.07173), which is a non-stationary signal decomposition method like the pioneering Empirical Mode Decomposition (EMD) method. Moreover, based on the MIF technique, we propose also a pre-processing method that allows to decorrelate and mean-center a hyperspectral dataset. The Cosine Similarity measure, which often fails in practice, appears to become a successful and outperforming classifier when equipped with such pre-processing method. We show some examples of the proposed methods when applied to real life problems.

math.NA↗
arXiv2015

Adaptive Local Iterative Filtering for Signal Decomposition and Instantaneous Frequency analysis

Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods, such as the empirical mode decomposition (EMD) technique pioneered by Huang et al., were developed by different research groups. These methods decompose a signal into a finite number of components on which the time-frequency analysis can be applied more effectively. In this paper we consider the iterative filters (IFs) approach as an alternative to EMD. We provide sufficient conditions on the filters that ensure the convergence of IFs applied to any $L^2$ signal. Then we propose a new technique, the Adaptive Local Iterative Filtering (ALIF) method, which uses the IFs strategy together with an adaptive and data driven filter length selection to achieve the decomposition. Furthermore we design smooth filters with compact support from solutions of Fokker-Planck equations (FP filters) that can be used within both IFs and ALIF methods. These filters fulfill the derived sufficient conditions for the convergence of the IFs algorithm. Numerical examples are given to demonstrate the performance and stability of IFs and ALIF techniques with FP filters. In addition, in order to have a complete and truly local analysis toolbox for non-linear and non-stationary signals, we propose a new definition for the instantaneous frequency which depends exclusively on local properties of a signal.

math.NA↗
arXiv2015

A sub-optimal solution for optimal control of linear systems with unmeasurable switching delays

We consider the optimal control design problem for discrete-time LTI systems with state feedback, when the actuation signal is subject to unmeasurable switching propagation delays, due to e.g. the routing in a multi-hop communication network and/or jitter. In particular, we set up a constrained optimization problem where the cost function is the worst-case $\mathcal{L}_2$ norm for all admissible switching delays. We first show how to model these systems as pure switching linear systems, and as main contribution of the paper we provide an algorithm to compute a sub-optimal solution.

eess.SY↗
arXiv2015

Multidimensional Iterative Filtering method for the decomposition of high-dimensional non-stationary signals

Iterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non-stationary and non-linear signals. Recently in [1] IF has been proved to be convergent for any $L^2$ signal and its stability has been also showed through examples. Furthermore in [1] the so called Fokker-Planck (FP) filters have been introduced. They are smooth at every point and have compact supports. Based on those results, in this paper we introduce the Multidimensional Iterative Filtering (MIF) technique for the decomposition and time-frequency analysis of non-stationary high-dimensional signals. And we present the extension of FP filters to higher dimensions. We illustrate the promising performance of MIF algorithm, equipped with high-dimensional FP filters, when applied to the decomposition of 2D signals. [1] A. Cicone, J. Liu, and H. Zhou, Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis, arXiv:1411.6051, 2014.

math.NA↗
arXiv2012

Lifted polytope methods for stability analysis of switching systems

We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of these two ideas allows us to introduce a pruning algorithm which can importantly reduce the computational burden. We prove several appealing theoretical properties of our methods like a finiteness computational result which extends a known result for unlifted sets of matrices, and provide numerical examples of their good behaviour.

math.OC↗