Jon Oñativia

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.

Computer-Aided Microcalcification Detection on Digital Breast Tomosynthesis Data: A Preliminary Evaluation

In this paper, we present a method for microcalcification detection on filtered back-projection reconstructed slices of breasts acquired on a Digital Breast Tomosynthesis system. Performance of the algorithm has been evaluated on a ground-truth database composed of 50 cases (13 lesions, 37 normals). Since the method is derived from an algorithm developed to detect microcalcifications on 2D digital mammograms, a comparison in terms of performances is provided leading to a discussion for future improvements.

Sequential local FRI sampling of infinite streams of Diracs

The theory of sampling signals with finite rate of innovation (FRI) has shown that it is possible to perfectly recover classes of non-bandlimited signals such as streams of Diracs from uniform samples. Most of previous papers, however, have to some extent only focused on the sampling of periodic or finite duration signals. In this paper we propose a novel method that is able to reconstruct infinite streams of Diracs, even in high noise scenarios. We sequentially process the discrete samples and output locations and amplitudes of the Diracs in real-time. We first establish conditions for perfect reconstruction in the noiseless case and then present the sequential algorithm for the noisy scenario. We also show that we can achieve a high reconstruction accuracy of 1000 Diracs for SNRs as low as 5dB.

Spike detection using FRI methods and protein calcium sensors: Performance analysis and comparisons

Fast and accurate detection of action potentials from neurophysiological data is key to the study of information processing in the nervous system. Previous work has shown that finite rate of innovation (FRI) theory can be used to successfully reconstruct spike trains from noisy calcium imaging data. This is due to the fact that calcium imaging data can be modeled as streams of decaying exponentials which are a subclass of FRI signals. Recent progress in the development of genetically encoded calcium indicators (GECIs) has produced protein calcium sensors that exceed the sensitivity of the synthetic dyes traditionally used in calcium imaging experiments. In this paper, we compare the suitability for spike detection of the kinetics of a new family of GECIs (the GCaMP6 family) with the synthetic dye Oregon Green BAPTA-1. We demonstrate the high performance of the FRI algorithm on surrogate data for each calcium indicator and we calculate the Cramér-Rao lower bound on the uncertainty of the position of a detected spike in calcium imaging data for each calcium indicator.

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.

Finite dimensional FRI

Traditional Finite Rate of Innovation (FRI) theory has considered the problem of sampling continuous-time signals. This framework can be naturally extended to the case where the input is a discrete-time signal. Here we present a novel approach which uses both the traditional FRI sampling scheme, based on the annihilating filter method, and the fact that in this new setup the null space of the problem to be solved is finite dimensional. In the noiseless scenario, we show that this new approach is able to perfectly recover the original signal at the critical sampling rate. We also present simulation results in the noisy scenario where this new approach improves performances in terms of the mean squared error (MSE) of the reconstructed signal when compared to the canonical FRI algorithms and compressed sensing (CS).

Approximate Strang-Fix: sampling infinite streams of Diracs with any kernel

In the last few years, several new methods have been developed for the sampling and the exact reconstruction of specific classes of non-bandlimited signals known as signals with finite rate of innovation (FRI). This is achieved by using adequate sampling kernels and reconstruction schemes. An important class of such kernels is the one made of functions able to reproduce exponentials. In this paper we review a new strategy for sampling these signals which is universal in that it works with any kernel. We do so by noting that meeting the exact exponential reproduction condition is too stringent a constraint, we thus allow for a controlled error in the reproduction formula in order to use the exponential reproduction idea with any kernel and develop a reconstruction method which is more robust to noise. We also present a novel method that is able to reconstruct infinite streams of Diracs, even in high noise scenarios. We sequentially process the discrete samples and output locations and amplitudes of the Diracs in real-time. In this context we also show that we can achieve a high reconstruction accuracy of 1000 Diracs for SNRs as low as 5dB.

Prosparse denoise: Prony's based sparse pattern recovery in the presence of noise

We present a novel algorithm - ProSparse Denoise - that can solve the sparsity recovery problem in the presence of noise when the dictionary is the union of Fourier and identity matrices. The algorithm is based on a proper use of Cadzow routine and Pronys method and exploits the duality of Fourier and identity matrices. The algorithm has low complexity compared to state of the art algorithms for sparse recovery since it relies on the Fast Fourier Transform (FFT) algorithm. We provide conditions on the noise that guarantees the correct recovery of the sparsity pattern. Our approach outperforms state of the art algorithms such as Basis Pursuit De-noise and Subspace Pursuit when the dictionary is the union of Fourier and identity matrices.

Sparsity pattern recovery using FRI methods

The problem of finding the sparse representation of a signal has attracted a lot of attention over the past years. In particular, uniqueness conditions and reconstruction algorithms have been established by relaxing a non-convex optimisation problem. The finite rate of innovation (FRI) theory is an alternative approach that solves the sparsity problem using algebraic methods based around Pronys algorithm. Recent extensions to this framework have shown that it is possible to recover sparse representations beyond the uniqueness limits, that is, finding all the possible sparse representations that fit the observation for the case of signals which are sparse in the union of Fourier and canonical bases. In this paper, we show the application of such methods to the case of the union of DCT and Haar basis. We present an extension that takes advantage of the even symmetry of the cosine functions to build an algorithm that can operate over the observed vector and in a dual domain. We also analyse the case of the union of frames. Simulation results confirm the validity of this new approach and show that it outperforms state of the art algorithms in a number scenarios.