Finite Rate Of Innovation Theory Research Articles

A General FRI Sampling System for Pulse Streams and the Multichannel Synchronization Method

Pulse streams are a kind of finite rate of innovation (FRI) signal that widely exist in many engineering applications. According to the FRI theory, nonconsecutive sampled Fourier coefficients (FCs) have better parameter estimation effects than the consecutive ones. In this brief, we propose a general FRI sampling system for pulse streams based on multichannel random modulation (MRM). Jointly using multichannel samples, multiple sets of consecutive FCs of distinct frequency bands can be analytically calculated by solving the least-squares problems. The minimum sampling rate for each channel is determined by the number of pulses rather than the pulse bandwidth. The proposed sampling system is general for pulses of distinct frequency bands, and we extend it to the frequency-agile radar (FAR). Besides, the multichannel synchronization problem is analyzed, and a calibration method when the pseudo-random sequences (PRSs) are not synchronized is proposed. Simulation experiments demonstrate the effectiveness of the proposed sampling system.

When de Prony Met Leonardo: An Automatic Algorithm for Chemical Element Extraction From Macro X-Ray Fluorescence Data

Macro X-ray Fluorescence (MA-XRF) scanning is an increasingly widely used technique for analytical imaging of paintings and other artworks. The datasets acquired must be processed to produce maps showing the distribution of the chemical elements that are present in the painting. Existing approaches require varying degrees of expert user intervention, in particular to select a list of target elements against which to fit the data. In this paper, we propose a novel approach that can automatically extract and identify chemical elements and their distributions from MA-XRF datasets. The proposed approach consists of three parts: 1) pre-processing steps, 2) pulse detection and model order selection based on Finite Rate of Innovation theory, and 3) chemical element estimation based on Cramer-Rao bounding techniques. The performance of our approach is assessed using MA-XRF datasets acquired from paintings in the collection of the National Gallery, London. The results presented show the ability of our approach to detect elements with weak X-ray fluorescence intensity and from noisy XRF spectra, to separate overlapping elemental signals and, excitingly, to aid visualisation of hidden underdrawing in a masterpiece by Leonardo da Vinci.

Sparse sampling: theory, methods and an application in neuroscience.

The current methods used to convert analogue signals into discrete-time sequences have been deeply influenced by the classical Shannon–Whittaker–Kotelnikov sampling theorem. This approach restricts the class of signals that can be sampled and perfectly reconstructed to bandlimited signals. During the last few years, a new framework has emerged that overcomes these limitations and extends sampling theory to a broader class of signals named signals with finite rate of innovation (FRI). Instead of characterising a signal by its frequency content, FRI theory describes it in terms of the innovation parameters per unit of time. Bandlimited signals are thus a subset of this more general definition. In this paper, we provide an overview of this new framework and present the tools required to apply this theory in neuroscience. Specifically, we show how to monitor and infer the spiking activity of individual neurons from two-photon imaging of calcium signals. In this scenario, the problem is reduced to reconstructing a stream of decaying exponentials.

Super-Resolution Sparse MIMO-OFDM Channel Estimation Based on Spatial and Temporal Correlations

This letter proposes a parametric sparse multiple input multiple output (MIMO)-OFDM channel estimation scheme based on the finite rate of innovation (FRI) theory, whereby super-resolution estimates of path delays with arbitrary values can be achieved. Meanwhile, both the spatial and temporal correlations of wireless MIMO channels are exploited to improve the accuracy of the channel estimation. For outdoor communication scenarios, where wireless channels are sparse in nature, path delays of different transmit-receive antenna pairs share a common sparse pattern due to the spatial correlation of MIMO channels. Meanwhile, the channel sparse pattern is nearly unchanged during several adjacent OFDM symbols due to the temporal correlation of MIMO channels. By simultaneously exploiting those MIMO channel characteristics, the proposed scheme performs better than existing state-of-the-art schemes. Furthermore, by joint processing of signals associated with different antennas, the pilot overhead can be reduced under the framework of the FRI theory.

A finite rate of innovation algorithm for fast and accurate spike detection from two-photon calcium imaging

Objective. Inferring the times of sequences of action potentials (APs) (spike trains) from neurophysiological data is a key problem in computational neuroscience. The detection of APs from two-photon imaging of calcium signals offers certain advantages over traditional electrophysiological approaches, as up to thousands of spatially and immunohistochemically defined neurons can be recorded simultaneously. However, due to noise, dye buffering and the limited sampling rates in common microscopy configurations, accurate detection of APs from calcium time series has proved to be a difficult problem. Approach. Here we introduce a novel approach to the problem making use of finite rate of innovation (FRI) theory (Vetterli et al 2002 IEEE Trans. Signal Process. 50 1417–28). For calcium transients well fit by a single exponential, the problem is reduced to reconstructing a stream of decaying exponentials. Signals made of a combination of exponentially decaying functions with different onset times are a subclass of FRI signals, for which much theory has recently been developed by the signal processing community. Main results. We demonstrate for the first time the use of FRI theory to retrieve the timing of APs from calcium transient time series. The final algorithm is fast, non-iterative and parallelizable. Spike inference can be performed in real-time for a population of neurons and does not require any training phase or learning to initialize parameters. Significance. The algorithm has been tested with both real data (obtained by simultaneous electrophysiology and multiphoton imaging of calcium signals in cerebellar Purkinje cell dendrites), and surrogate data, and outperforms several recently proposed methods for spike train inference from calcium imaging data.

Compressive Sampling of EEG Signals with Finite Rate of Innovation

Analyses of electroencephalographic signals and subsequent diagnoses can only be done effectively on long term recordings that preserve the signals' morphologies. Currently, electroencephalographic signals are obtained at Nyquist rate or higher, thus introducing redundancies. Existing compression methods remove these redundancies, thereby achieving compression. We propose an alternative compression scheme based on a sampling theory developed for signals with a finite rate of innovation (FRI) which compresses electroencephalographic signals during acquisition. We model the signals as FRI signals and then sample them at their rate of innovation. The signals are thus effectively represented by a small set of Fourier coefficients corresponding to the signals' rate of innovation. Using the FRI theory, original signals can be reconstructed using this set of coefficients. Seventy-two hours of electroencephalographic recording are tested and results based on metrices used in compression literature and morphological similarities of electroencephalographic signals are presented. The proposed method achieves results comparable to that of wavelet compression methods, achieving low reconstruction errors while preserving the morphologiies of the signals. More importantly, it introduces a new framework to acquire electroencephalographic signals at their rate of innovation, thus entailing a less costly low-rate sampling device that does not waste precious computational resources.