Sparsity-Aware 3-D ToF Sensing

Paredes, Alvaro Lopez; Conde, Miguel Heredia; Loffeld, Otmar

doi:10.1109/jsen.2023.3234533

Cited by 4 publications

(5 citation statements)

References 63 publications

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“…The proposed coding scheme, called gradient-Combinatorial (GComb) [2], iteratively adds [⃗ a j ] n j=1 , and consists of the following steps:…”

Section: Methodsmentioning

confidence: 99%

“…If the added non-zero element yields µ dif = 1, we remove it from the set of candidates. This evaluation step translates into a deterministic arrangement of [⃗ a j ] n j=1 , and can be applied to any other methodology such as LDPC-PEG [2]. GComb yields an upper bound for γSR such that µ < 1.…”

Section: Methodsmentioning

confidence: 99%

“…At ZESS, we have designed a rotary PB-ToF camera that allows us to implement the presented computational sensing approaches to bring long-range wide-area ToF imaging to a new level of accuracy [2]. The design parameters of our prototype used in this numerical simulation are shown in Table I.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Random and Hadamard-derived (0,1)-binary codes may be used in the modulation/demodulation schemes [2], as the resulting sensing matrices ensure good recoverability properties for moderate aspect ratios (η = m n ), as shown in Fig. 2.…”

Section: Introductionmentioning

confidence: 99%

“…However, these schemes may lead to µ = 1 for η ≪ 1. To solve that issue, some deterministic approaches such as the ones which make use of Low-Density Parity-Check (LDPC) codes via Progressive-Edge Growth (PEG) [3] were explored in [2]. PEG works iteratively per columns, adding a fixed number of non-zero elements at the locations which locally maximize the girth of the associated Tanner graph.…”

Section: Introductionmentioning

confidence: 99%

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Sparsity-aware 3D ToF Sensing

Paredes¹,

Loffeld²,

Conde³

2022

Preprint

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In this work, several ToF sensing schemes which tackle the challenge of obtaining high angular resolution and long ranges in nearly real-time, with relatively simple implementation and low associated computational load, are proposed. Sliced Orthogonal Matching Pursuit (OMP) divides the spatial domain in a number of partitions which ensure an efficient projection of the scene by optimizing the inter-column coherence of the sensing matrices. The signals are preliminarily localized within the partitions and OMP is then applied to recover depth and amplitude in a refined spatial domain. The preliminary set of measurements reduces the effective domain of the signal, lowers the processing times, and improves the sensing accuracy. Several methodologies are described for the construction of the sensing matrices, such as Low-Density Parity-Check codes via Progressive Edge Growth (LDPC-PEG), and random permutations of (0,1)-binary columns generated as combinations without repetition of a fixed number of non?zero elements for each column. Furthermore, we extend the previous schemes accounting for the raising and falling edges in order to avoid any possible coincidence which may degrade the coherence. Then, the upper super-resolution limit is studied accounting for the Instrument Response Function (IRF) of the ToF sensor. Zoned APEG extends the applicability of Adaptive Progressive Edge Algorithm (APEG) to more practical illumination systems by considering several groups of signals, arising from different areas of the sensor array, during the adaptation of the sensing matrices. The signals are then individually retrieved for each pixel via OMP over the identified joint signal support.

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“…The proposed coding scheme, called gradient-Combinatorial (GComb) [2], iteratively adds [⃗ a j ] n j=1 , and consists of the following steps:…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sparsity-aware 3D ToF Sensing

Paredes¹,

Loffeld²,

Conde³

2022

Preprint

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Coherence, Distance and Error: Understanding Coded Demodulation in PB-ToF Imaging

Paredes,

Gutierrez-Barragan,

Conde

2024

2024 International Workshop on the Theory of Computational Sensing and Its Applications to Radar, Multimodal Sensing and Imagin

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One of the main objectives in coded Time-of-Flight is to precisely determine the position of the recovered target(s) with very few measurements or, in other words, to increase the resolution of the sensing system at high frame rates. In this scenario, we may cope with highly-coherent sensing matrices, i. e., there exist several columns very similar to each other. This may yield severe errors during the depth's retrieval. In this paper, we show that the foreseen potential (probable) mismatches in the support estimation are related to the distance between the most cross-correlated columns over the sensing matrix, and propose a, to our knowledge, new metric which allows for estimating the average (absolute) recovery error. The metric is given by the mean absolute distance between each column and the most cross-correlated columns over the sensing matrix. We numerically evaluate various state-of-the-art demodulation schemes, and demonstrate that our metric reliably provides an estimation of their recovery performance, and complements other metrics traditionally used in Computational Sensing.

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