One-bit Unlimited Sampling

Graf, Olga; Bhandari, Ayush; Krahmer, Felix

doi:10.1109/icassp.2019.8683266

Cited by 28 publications

(22 citation statements)

References 15 publications

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“…Sparse recovery from modulo samples limited to two modulo folds was discussed in [23]. Further on, Unlimited Sampling was extended to one-bit uniform samples [24]. The USF reconstruction was demonstrated theoretically and numerically for samples corrupted by bounded noise [3], and also for imaging data [7].…”

Section: Related Workmentioning

confidence: 99%

“…Thresholding is a well-known approach for solving inverse problems [30]- [32]. Its practical utility in USF was shown by filtering the data with a kernel such as a B-spline [24] or a wavelet [33]. However, given that the folding times of the modulo encoder can get arbitrarily close for any input, no work so far has been able to provide guarantees in this context (see Section II-A).…”

Section: Related Workmentioning

confidence: 99%

“…A different reconstruction approach for the ideal modulo encoder consists of filtering the modulo output with a high-pass kernel and thresholding the filtered signal to detect the folding times. The filtering operation cancels out the bandlimited input and results in high amplitude pulses centered in the folding times [24]. Given that the pulses have a non-zero support size, this approach introduces the challenge of ensuring a minimal separation between folding times.…”

Section: A the Ideal Modulo Encodermentioning

confidence: 99%

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The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments

Florescu,

Krahmer,

Bhandari

2021

Preprint

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The Unlimited Sensing Framework (USF) was recently introduced to overcome the sensor saturation bottleneck in conventional digital acquisition systems. At its core, the USF allows for high-dynamic-range (HDR) signal reconstruction by converting a continuous-time signal into folded, low-dynamic-range (LDR), modulo samples. HDR reconstruction is then carried out by algorithmic unfolding of the folded samples. In hardware, however, implementing an ideal modulo folding requires careful calibration, analog design and high precision. At the interface of theory and practice, this paper explores a computational sampling strategy that relaxes strict hardware requirements by compensating them via a novel, mathematically guaranteed recovery method. Our starting point is a generalized model for USF. The generalization relies on two new parameters modeling hysteresis and folding transients in addition to the modulo threshold. Hysteresis accounts for the mismatch between the reset threshold and the amplitude displacement at the folding time and we refer to a continuous transition period in the implementation of a reset as folding transient. Both these effects are motivated by our hardware experiments and also occur in previous, domain-specific applications.We show that the effect of hysteresis is beneficial for the USF and we leverage it to derive the first recovery guarantees in the context of our generalized USF model. Additionally, we show how the proposed recovery can be directly generalized for the case of lower sampling rates. Our theoretical work is corroborated by hardware experiments that are based on a hysteresis enabled, modulo ADC testbed comprising off-the-shelf electronic components. Thus, by capitalizing on a collaboration between hardware and algorithms, our paper enables an end-to-end pipeline for HDR sampling allowing more flexible hardware implementations.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: A the Ideal Modulo Encodermentioning

confidence: 99%

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The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments

Florescu,

Krahmer,

Bhandari

2021

Preprint

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“…The recovery is theoretically guaranteed. Further on, Unlimited Sampling was extended to one-bit uniform samples [19,20]. Recently, hardware implementation of the Unlimited Sampling approach was reported and verified in [21].…”

Section: Introductionmentioning

confidence: 99%

Event-Driven Modulo Sampling

Florescu

Krahmer

Bhandari

2021

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

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In contrast to Shannon sampling theory, where measurements are recorded at equally-spaced time instants, event-driven sampling records values at non-uniform instants dependent on the input. However, both sampling schemes are subject to input dynamic range constraints. This represents a fundamental bottleneck, which can only be alleviated via adjustments in the encoder architecture. Here we explore an alternative strategy based on the recent work on Unlimited Sampling theory, which uses a modulo non-linearity to guarantee a predefined input amplitude range. We propose a cascade model comprising a modulo non-linearity in series with an integrateand-fire (IF) event-driven encoder. The modulo component does not act on inputs within the IF dynamic range, thus our model is fully compatible with the existing IF methodology. For inputs outside the IF dynamic range, the modulo output is discontinuous, and it currently cannot be recovered from the IF output with existing methods. We introduce theoretical conditions for which the input of the proposed cascade model can be recovered with arbitrary precision. Through numerical simulations, we show the performance of the reconstruction algorithm. The proposed methodology paves the way for a new generation of event-driven models suitable for a much wider range of applications.

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“…The most frequently used algorithms in compressive sensing are adjusted to the quantization effect arXiv:1907.01078v1 [cs.IT] 1 Jul 2019 in [24]. For the case of one-bit unlimited sampling, a quantization approach using the one-bit modulo samples, [25] shows the bounds of the reconstruction error.…”

Section: Introductionmentioning

confidence: 99%

Quantization in Compressive Sensing: A Signal Processing Approach

et al. 2020

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Influence of the finite-length registers and quantization effects on the reconstruction of sparse and approximately sparse signals is analyzed in this paper. For the nonquantized measurements, the compressive sensing (CS) framework provides highly accurate reconstruction algorithms that produce negligible errors when the reconstruction conditions are met. However, hardware implementations of signal processing algorithms involve the finite-length registers and quantization of the measurements. An analysis of the effects related to the measurements quantization with an arbitrary number of bits is the topic of this paper. A unified mathematical model for the analysis of the quantization noise and the signal nonsparsity on the CS reconstruction is presented. An exact formula for the expected energy of error in the CS-based reconstructed signal is derived. The theory is validated through various numerical examples with quantized measurements, including the cases of approximately sparse signals, noise folding, and floating-point arithmetics.

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One-bit Unlimited Sampling

Cited by 28 publications

References 15 publications

The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments

The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments

Event-Driven Modulo Sampling

Quantization in Compressive Sensing: A Signal Processing Approach

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