Super-resolved time-of-flight sensing via FRI sampling theory

Bhandari, Ayush; Wallace, Andrew M.; Raskar, Ramesh

doi:10.1109/icassp.2016.7472430

Cited by 24 publications

(51 citation statements)

References 18 publications

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“…In many cases, ψ is a smooth and compactly supported pulse/function [12], [14], [25]. The next proposition states a sufficient condition for smoothness (or differentiability) of a function ψ in the SAFT domain.…”

Section: E Sparse Signals and Smooth Time-limited Kernelsmentioning

confidence: 99%

“…These are signals which are described by countable degrees of freedom, per unit time and model a broad class of signals. The FRI sampling has been applied to a number of interesting applications such as channel estimation [24], radar [15]- [17], timeresolved imaging [14], [17], [25], sparse recovery on a sphere [26], image feature detection [27]- [29], medical imaging [18], [19], [30], [31], tomography [32], astronomy [33], spectroscopy [34], unlimited sampling architecture [35], [36] and inverse source problems [37], [38].…”

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confidence: 99%

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Sampling and Super Resolution of Sparse Signals Beyond the Fourier Domain

Bhandari

Eldar

2019

IEEE Trans. Signal Process.

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Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the natural choice. For example, in holography, lowpass projections of sparse signals are obtained in the Fresnel domain. Similarly, time-varying system identification relies on low-pass projections on the space of linear frequency modulated signals. In this paper, we study the recovery of sparse signals from low-pass projections in the Special Affine Fourier Transform domain (SAFT). The SAFT parametrically generalizes a number of well known unitary transformations that are used in signal processing and optics. In analogy to the Shannon's sampling framework, we specify sampling theorems for recovery of sparse signals considering three specific cases: (1) sampling with arbitrary, bandlimited kernels, (2) sampling with smooth, timelimited kernels and, (3) recovery from Gabor transform measurements linked with the SAFT domain. Our work offers a unifying perspective on the sparse sampling problem which is compatible with the Fourier, Fresnel and Fractional Fourier domain based results. In deriving our results, we introduce the SAFT series (analogous to the Fourier series) and the short time SAFT, and study convolution theorems that establish a convolution-multiplication property in the SAFT domain.Preliminary ideas leading to this manuscript were presented in parts at ICASSP 2015 [1] and 2016 [2]. A. Bhandari is with the Massachusetts

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Section: E Sparse Signals and Smooth Time-limited Kernelsmentioning

confidence: 99%

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confidence: 99%

Sampling and Super Resolution of Sparse Signals Beyond the Fourier Domain

Bhandari

Eldar

2019

IEEE Trans. Signal Process.

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“…Given the fact that z ∼ N (µ z , σ 2 z ) 2 and considering the measurement model given by (6), we can calculate the closed form expressions for the scalar measurement updates in (12). These terms are computed according to Table 1.…”

Section: B Nonlinear Steps In the Updatesmentioning

confidence: 99%

Generalized Approximate Message Passing for Unlimited Sampling of Sparse Signals

Musa

Jung

Goertz

2018

2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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In this paper we consider the generalized approximate message passing (GAMP) algorithm for recovering a sparse signal from modulo samples of randomized projections of the unknown signal. The modulo samples are obtained by a self-reset (SR) analog to digital converter (ADC). Additionally, in contrast to previous work on SR ADC, we consider a scenario where the compressed sensing (CS) measurements (i.e., randomized projections) are sent through a communication channel, namely an additive white Gaussian noise (AWGN) channel before being quantized by a SR ADC. To show the effectiveness of the proposed approach, we conduct Monte-Carlo (MC) simulations for both noiseless and noisy case. The results show strong ability of the proposed algorithm to fight the nonlinearity of the SR ADC, as well as the possible additional distortion introduced by the AWGN channel.Index Terms-Generalized approximate message passing, selfreset analog to digital converter, noisy channel, compressed sensing, Bernoulli-Gaussian mixture

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“…Due to physical constraints inherent to all electro-optical systems, it is reasonable to approximate the probing signal as a bandlimited function [9], [25]. We use L-term Fourier series with basis functions u n (ω 0 t) def = e ω0nt , ω 0 T = 2π, to approximate p with,…”

Section: A Bandlimited Approximation Of Probing Functionmentioning

confidence: 99%

“…is an ill-posed problem. Each year, a number of papers [3]- [8] [9] where t k is a non-linear argument in (3). As a result, our goal is to recover the intensities of a sparse signal.…”

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Sampling without time: Recovering echoes of light via temporal phase retrieval

Bhandari

Bourquard

Raskar

2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple echoes of light from its low-pass filtered and auto-correlated, time-domain measurements. Our work is closely related to the topic of sparse phase retrieval and in this context, we discuss the advantage of phase-free measurements. While this problem is ill-posed, cues based on physical constraints allow for its appropriate regularization. We validate our theory with experiments based on customized, optical time-of-flight imaging sensors. What singles out our approach is that our sensing method allows for temporal phase retrieval as opposed to the usual case of spatial phase retrieval. Preliminary experiments and results demonstrate a compelling capability of our phase-retrieval based imaging device.

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Super-resolved time-of-flight sensing via FRI sampling theory

Cited by 24 publications

References 18 publications

Sampling and Super Resolution of Sparse Signals Beyond the Fourier Domain

Sampling and Super Resolution of Sparse Signals Beyond the Fourier Domain

Generalized Approximate Message Passing for Unlimited Sampling of Sparse Signals

Sampling without time: Recovering echoes of light via temporal phase retrieval

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