Approximate reconstruction of bandlimited functions for the integrate and fire sampler

Feichtinger, Hans G.; Prı́ncipe, José C.; Romero, José Luis; Alvarado, Alexander; Velasco, Gino Angelo

doi:10.1007/s10444-011-9180-9

Cited by 50 publications

(22 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The deterministic spike model consists of a continuous RBF model in the form (20) combined with an LIF sampler that converts the RBF into a square wave function. The LIF sampler developed in [28] for the approximate reconstruction of bandlimited functions is adopted, which converts any continuous signal f (t) into a square wave function by integrating it against an averaging function u k,z (t). The integrated result is compared to a positive threshold and a negative threshold, such that when either one of the two thresholds is reached, a pulse is generated at time t k = z.…”

Section: Deterministic Spike Modelmentioning

confidence: 99%

“…The value of the integrator is then reset and the process repeats. In this paper, the averaging function u k,z (t) is chosen to be the exponential e α(t−z) X [tk,z] , where X I is the characteristic function of I and α > 0 is a constant that models the leakage of the integrator, as due to practical implementations [28]. Then, the LIF sampler firing condition that generates the square wave (or sequence of pulses) is…”

Section: Deterministic Spike Modelmentioning

confidence: 99%

See 1 more Smart Citation

A Radial Basis Function Spike Model for Indirect Learning via Integrate-and-Fire Sampling and Reconstruction Techniques

Zhang

Foderaro

Henriquez

et al. 2012

Advances in Artificial Neural Systems

View full text Add to dashboard Cite

This paper presents a deterministic and adaptive spike model derived from radial basis functions and a leaky integrate-and-fire sampler developed for training spiking neural networks without direct weight manipulation. Several algorithms have been proposed for training spiking neural networks through biologically-plausible learning mechanisms, such as spike-timing-dependent synaptic plasticity and Hebbian plasticity. These algorithms typically rely on the ability to update the synaptic strengths, or weights, directly, through a weight update rule in which the weight increment can be decided and implemented based on the training equations. However, in several potential applications of adaptive spiking neural networks, including neuroprosthetic devices and CMOS/memristor nanoscale neuromorphic chips, the weights cannot be manipulated directly and, instead, tend to change over time by virtue of the pre- and postsynaptic neural activity. This paper presents an indirect learning method that induces changes in the synaptic weights by modulating spike-timing-dependent plasticity by means of controlled input spike trains. In place of the weights, the algorithm manipulates the input spike trains used to stimulate the input neurons by determining a sequence of spike timings that minimize a desired objective function and, indirectly, induce the desired synaptic plasticity in the network.

show abstract

Section: Deterministic Spike Modelmentioning

confidence: 99%

Section: Deterministic Spike Modelmentioning

confidence: 99%

A Radial Basis Function Spike Model for Indirect Learning via Integrate-and-Fire Sampling and Reconstruction Techniques

Zhang

Foderaro

Henriquez

et al. 2012

Advances in Artificial Neural Systems

View full text Add to dashboard Cite

show abstract

“…State-of-the-art signal reconstruction methods rely on assumptions or estimations of characteristics like spectral moments or signal bandwidth [9,[11][12][13][14]. Deviations or inaccurate estimates can impair the quality of the signal reconstruction.…”

Section: Motivationmentioning

confidence: 99%

“…For applications as sampler in electronic systems see, e.g., [6,7]. For a survey regarding the recovery problem see, e.g., [8,9].…”

Section: Introductionmentioning

confidence: 99%

On Quasi-Isometry of Threshold-Based Sampling

Moser

Lunglmayr

2019

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

The problem of isometry for threshold-based sampling such as integrate-andfire (IF) or send-on-delta (SOD) is addressed. While for uniform sampling the Parseval theorem provides isometry and makes the Euclidean metric canonical, there is no analogy for threshold-based sampling. The relaxation of the isometric postulate to quasi-isometry, however, allows the discovery of the underlying metric structure of threshold-based sampling. This paper characterizes this metric structure making Hermann Weyl's discrepancy measure canonical for threshold-based sampling.

show abstract

“…Time encoding and decoding has been studied for different signal classes, from bandlimited signals [3,4] to the more general shift-invariant subspaces [5] and even to some classes of finite rate of innovation signals [6], mostly by relating the recorded times to irregular samples and performing reconstruction from irregular samples [7,8].…”

Section: Introductionmentioning

confidence: 99%

Encoding and Decoding Mixed Bandlimited Signals Using Spiking Integrate-and-Fire Neurons

Adam

Scholefield

Vetterli

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

Conventional sampling focuses on encoding and decoding bandlimited signals by recording signal amplitudes at known time points. Alternately, sampling can be approached using biologically-inspired schemes. Among these are integrateand-fire time encoding machines (IF-TEMs). They behave like simplified versions of spiking neurons and encode their input using spike times rather than amplitudes.Moreover, when multiple of these neurons jointly process a set of mixed signals, they form one layer in a feedforward spiking neural network. In this paper, we investigate the encoding and decoding potential of such a layer.We propose a setup to sample a set of bandlimited signals, by mixing them and sampling the result using different IF-TEMs. We provide conditions for perfect recovery of the set of signals from the samples in the noiseless case, and suggest an algorithm to perform the reconstruction.

show abstract

Approximate reconstruction of bandlimited functions for the integrate and fire sampler

Cited by 50 publications

References 11 publications

A Radial Basis Function Spike Model for Indirect Learning via Integrate-and-Fire Sampling and Reconstruction Techniques

A Radial Basis Function Spike Model for Indirect Learning via Integrate-and-Fire Sampling and Reconstruction Techniques

On Quasi-Isometry of Threshold-Based Sampling

Encoding and Decoding Mixed Bandlimited Signals Using Spiking Integrate-and-Fire Neurons

Contact Info

Product

Resources

About