Multi-channel Time Encoding for Improved Reconstruction of Bandlimited Signals

Adam, Karen; Scholefield, Adam; Vetterli, Martin

doi:10.1109/icassp.2019.8682361

Cited by 17 publications

(13 citation statements)

References 18 publications

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“…We have thus shown that using M time encoding machines to encode a 2Ω-bandlimited signal x(t) allows a bandwidth Ω which is M times larger than in the single channel case, no matter how the shifts between the machines are configured, as long as they are all nonzero. As already stated, we had shown in [22] that the bandwidth could become M times larger, but only if the machines were configured in such a way that their integrators had equally spaced values. In other words, if we denote y i (t) to be the value of the integrator of machine i, then we required, ∀i = 1 · · · M − 1,…”

Section: Uniqueness Of M-channel Reconstruction Using Pocsmentioning

confidence: 67%

Sampling and Reconstruction of Bandlimited Signals With Multi-Channel Time Encoding

Adam

Scholefield

Vetterli

2020

IEEE Trans. Signal Process.

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Sampling is classically performed by recording the amplitude of the input at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the devices have an unknown shift in their clocks.Alternatively, one can record the times at which a signal (or its integral) crosses given thresholds. This can model integrateand-fire neurons, for example, and has been studied by Lazar and Tóth under the name of "Time Encoding Machines". This sampling method is closer to what is found in nature.In this paper, we show that, when using time encoding machines, reconstruction from multiple channels has a more intuitive solution, and does not require the knowledge of the shifts between machines. We show that, if single-channel time encoding can sample and perfectly reconstruct a 2Ω-bandlimited signal, then M -channel time encoding can sample and perfectly reconstruct a signal with M times the bandwidth. Furthermore, we present an algorithm to perform this reconstruction and prove that it converges to the correct unique solution, in the noiseless case, without knowledge of the relative shifts between the machines. This is quite unlike classical multi-channel sampling, where unknown shifts between sampling devices pose a problem for perfect reconstruction.

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Section: Uniqueness Of M-channel Reconstruction Using Pocsmentioning

confidence: 67%

Sampling and Reconstruction of Bandlimited Signals With Multi-Channel Time Encoding

Adam

Scholefield

Vetterli

2020

IEEE Trans. Signal Process.

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“…Given these constraints on the signal we can also derive the minimum possible value of |D| by substituting x0 = −xmin and x i =0 = xmax into equation (11). This can then be used to determine the appropriate trigger mark, CT < |D| to generate a given number of samples within the interval [t0, t0 + t * ].…”

Section: Conditions For Guaranteed Spikingmentioning

confidence: 99%

“…[8,9]. Time encoding systems have been previously used for reconstructing signals in shift-invariant spaces [10][11][12][13][14][15], as well as FRI signals in [16][17][18][19] using exponential spline sampling kernels and in [20] using hyperbolic secant kernels.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Reconstruction from Integrate-and-Fire Neurons with Alpha Synaptic Activation

Hilton

Alexandru

Dragotti

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Time encoding of continuous time signals is an alternative to classical sampling paradigms. The signal is encoded in the timing of output samples rather than their amplitudes. Of particular interest are integrate-and-fire time encoding machines (IF-TEM) for sampling signals with finite rate of innovation (FRI). In contrast to stateof-the-art methods we propose an IF-TEM where we employ a biologically inspired and smooth sampling kernel, the alpha synaptic function, and show that perfect reconstruction can be achieved using this kernel. Furthermore, we derive conditions on the input signal, a train of scaled Diracs, such that not only can we guarantee the generation of useful samples, even when the Diracs have arbitrary sign, but also that these useful samples can be determined from amongst the non-useful samples. Thus, reconstruction of signals satisfying these conditions is always possible.

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“…First, we review time encoding machines (TEMs), which are the ideal event-based sensor [7,12]. The input-output relationship of an integrateand-fire TEM follow similar rules to that of nonuniform sampling [13,14], and thus results in interesting consequences when it comes to single-signal multi-channel time encoding [15,16].…”

Section: Introductionmentioning

confidence: 99%

Asynchrony Increases Efficiency: Time Encoding of Videos and Low-Rank Signals

Adam

Scholefield

Vetterli

2022

IEEE Trans. Signal Process.

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In event-based sensing, many sensors independently and asynchronously emit events when there is a change in their input. Event-based sensing can present significant improvements in power efficiency when compared to traditional sampling, because (1) the output is a stream of events where the important information lies in the timing of the events, and (2) the sensor can easily be controlled to output information only when interesting activity occurs at the input.Moreover, event-based sampling can often provide better resolution than standard uniform sampling. Not only does this occur because individual event-based sensors have higher temporal resolution [1], it also occurs because the asynchrony of events within a sensor and therefore across sensors allows for less redundant and more informative encoding. We would like to explain how such curious results come about.To do so, we use ideal time encoding machines as a proxy for event-based sensors. We explore time encoding of signals with low rank structure, and apply the resulting theory to video. We then see how the asynchronous firing across time encoding machines can couple spatial sampling density with temporal resolution, leading to better reconstruction, whereas, in frame-based video, temporal resolution depends solely on the frame-rate and spatial resolution solely on the pixel grid used.

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Multi-channel Time Encoding for Improved Reconstruction of Bandlimited Signals

Cited by 17 publications

References 18 publications

Sampling and Reconstruction of Bandlimited Signals With Multi-Channel Time Encoding

Sampling and Reconstruction of Bandlimited Signals With Multi-Channel Time Encoding

Guaranteed Reconstruction from Integrate-and-Fire Neurons with Alpha Synaptic Activation

Asynchrony Increases Efficiency: Time Encoding of Videos and Low-Rank Signals

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