37 results found
Bhandari A, Krahmer F, Poskitt T, 2021, Unlimited sampling from theory to practice: fourier-prony recovery and prototype ADC, IEEE Transactions on Signal Processing, ISSN: 1053-587X
Following the Unlimited Sampling strategy to alleviate the omnipresent dynamic range barrier, we study the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware implementation considerations. Our starting point is a class of non-idealities that we observe in prototyping an unlimited sampling based analog-to-digital converter. To address these non-idealities, we provide a new Fourier domain recovery algorithm. Our approach is validated both in theory and via extensive experiments on our prototype analog-to-digital converter, providing the first demonstration of unlimited sampling for data arising from real hardware, both for the current and previous approaches. Advantages of our algorithm include that it is agnostic to the modulo threshold and it can handle arbitrary folding times. We expect that the end-to-end realization studied in this paper will pave the path for exploring the unlimited sampling methodology in a number of real world applications.
Bouis V, Krahmer F, Bhandari A, 2021, Multidimensional Unlimited Sampling: A Geometrical Perspective, 28th European Signal Processing Conference (EUSIPCO), Publisher: IEEE, Pages: 2314-2318, ISSN: 2076-1465
Bhandari A, Beckmann M, Krahmer F, 2021, The Modulo Radon Transform and its Inversion, 28th European Signal Processing Conference (EUSIPCO), Publisher: IEEE, Pages: 770-774, ISSN: 2076-1465
Fernandez-Menduina S, Krahmer F, Leus G, et al., 2021, DoA Estimation via Unlimited Sensing, 28th European Signal Processing Conference (EUSIPCO), Publisher: IEEE, Pages: 1866-1870, ISSN: 2076-1465
Bhandari A, Krahmer F, Raskar R, 2020, On unlimited sampling and reconstruction, IEEE Transactions on Signal Processing, Vol: 69, Pages: 3827-3839, ISSN: 1053-587X
Shannon's sampling theorem is one of the cornerstone topics that is well understood and explored, both mathematically and algorithmically. That said, practical realization of this theorem still suffers from a severe bottleneck due to the fundamental assumption that the samples can span an arbitrary range of amplitudes. In practice, the theorem is realized using so-called analog--to--digital converters (ADCs) which clip or saturate whenever the signal amplitude exceeds the maximum recordable ADC voltage thus leading to a significant information loss. In this paper, we develop an alternative paradigm for sensing and recovery, called the Unlimited Sampling Framework. It is based on the observation that when a signal is mapped to an appropriate bounded interval via a modulo operation before entering the ADC, the saturation problem no longer exists, but one rather encounters a different type of information loss due to the modulo operation. Such an alternative setup can be implemented, for example, via so-called folding or self-reset ADCs, as they have been proposed in various contexts in the circuit design literature. The key task that we need to accomplish in order to cope with this new type of information loss is to recover a bandlimited signal from its modulo samples. In this paper we derive conditions when perfect recovery is possible and complement them with a stable recovery algorithm. The sampling density required to guarantee recovery is independent of the maximum recordable ADC voltage and depends on the signal bandwidth only. Our recovery guarantees extend to measurements affected by bounded noise, which includes the case of round-off quantization. Numerical experiments validate our approach. For example, it is possible to recover functions with amplitudes orders of magnitude higher than the ADC's threshold from quantized modulo samples upto the unavoidable quantization error. Applications of the unlimited sampling paradigm can be found in a number of fields su
Bhandari A, Conde MH, Loffeld O, 2020, One-Bit Time-Resolved Imaging, IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, Vol: 42, Pages: 1630-1641, ISSN: 0162-8828
Bhandari A, Graf O, Krahmer F, et al., 2020, ONE-BIT SAMPLING IN FRACTIONAL FOURIER DOMAIN, IEEE International Conference on Acoustics, Speech, and Signal Processing, Publisher: IEEE, Pages: 9140-9144, ISSN: 1520-6149
Beckmann M, Krahmer F, Bhandari A, 2020, HDR TOMOGRAPHY VIA MODULO RADON TRANSFORM, IEEE International Conference on Image Processing (ICIP), Publisher: IEEE, Pages: 3025-3029, ISSN: 1522-4880
Bhandari A, Krahmer F, 2020, HDR IMAGING FROM QUANTIZATION NOISE, IEEE International Conference on Image Processing (ICIP), Publisher: IEEE, Pages: 101-105, ISSN: 1522-4880
Bhandari A, Zayed AI, 2019, Shift-invariant and sampling spaces associated with the special aline Fourier transform, APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, Vol: 47, Pages: 30-52, ISSN: 1063-5203
Bhandari A, Eldar YC, 2019, Sampling and super resolution of sparse signals beyond the Fourier domain, IEEE Transactions on Signal Processing, Vol: 67, Pages: 1508-1521, ISSN: 1053-587X
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, low-pass 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, time-limited 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.
Batenkov D, Bhandari A, Blu T, 2019, RETHINKING SUPER-RESOLUTION: THE BANDWIDTH SELECTION PROBLEM, 44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Publisher: IEEE, Pages: 5087-5091, ISSN: 1520-6149
Graf O, Bhandari A, Krahmer F, 2019, ONE-BIT UNLIMITED SAMPLING, 44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Publisher: IEEE, Pages: 5102-5106, ISSN: 1520-6149
Bhandari A, Krahmer F, 2019, On Identifiability in Unlimited Sampling, 13th International Conference on Sampling Theory and Applications (SampTA), Publisher: IEEE
Bhandari A, Zayed AI, 2018, Convolution and Product Theorems for the Special Affine Fourier Transform, Frontiers in Orthogonal Polynomials and q-Series, Publisher: WORLD SCIENTIFIC, Pages: 119-137
Bhandari A, Krahmer F, Raskar R, 2018, Unlimited Sampling of Sparse Sinusoidal Mixtures, IEEE International Symposium on Information Theory (ISIT), Publisher: IEEE, Pages: 336-340
Bhandari A, Krahmer F, Raskar R, 2017, On unlimited sampling, 2017 International Conference on Sampling Theory and Applications (SampTA), Publisher: IEEE, Pages: 31-35
Shannon's sampling theorem provides a link between the continuous and the discrete realms stating that bandlimited signals are uniquely determined by its values on a discrete set. This theorem is realized in practice using so called analog-to-digital converters (ADCs). Unlike Shannon's sampling theorem, the ADCs are limited in dynamic range. Whenever a signal exceeds some preset threshold, the ADC saturates, resulting in aliasing due to clipping. The goal of this paper is to analyze an alternative approach that does not suffer from these problems. Our work is based on recent developments in ADC design, which allow for ADCs that reset rather than to saturate, thus producing modulo samples. An open problem that remains is: Given such modulo samples of a bandlimited function as well as the dynamic range of the ADC, how can the original signal be recovered and what are the sufficient conditions that guarantee perfect recovery? In this paper, we prove such sufficiency conditions and complement them with a stable recovery algorithm. Our results are not limited to certain amplitude ranges, in fact even the same circuit architecture allows for the recovery of arbitrary large amplitudes as long as some estimate of the signal norm is available when recovering. Numerical experiments that corroborate our theory indeed show that it is possible to perfectly recover function that takes values that are orders of magnitude higher than the ADC's threshold.
Bhandari A, Bourquard A, Raskar R, 2017, SAMPLING WITHOUT TIME: RECOVERING ECHOES OF LIGHT VIA TEMPORAL PHASE RETRIEVAL, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 3829-3833, ISSN: 1520-6149
Bhandari A, Blu T, 2017, FRI SAMPLING AND TIME-VARYING PULSES: SOME THEORY AND FOUR SHORT STORIES, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 3804-3808, ISSN: 1520-6149
Bhandari A, Raskar R, 2016, Signal processing for time-of-flight imaging sensors: an introduction to inverse problems in computational 3-D imaging, IEEE Signal Processing Magazine, Vol: 33, Pages: 45-58, ISSN: 1053-5888
Time-of-flight (ToF) sensors offer a cost-effective and realtime solution to the problem of three-dimensional (3-D) imaging-a theme that has revolutionized our sceneunderstanding capabilities and is a topic of contemporary interest across many areas of science and engineering. The goal of this tutorial-style article is to provide a thorough understanding of ToF imaging systems from a signal processing perspective that is useful to all application areas. Starting with a brief history of the ToF principle, we describe the mathematical basics of the ToF image-formation process, for both time- and frequency-domain, present an overview of important results within the topic, and discuss contemporary challenges where this emerging area can benefit from the signal processing community. In particular, we examine case studies where inverse problems in ToF imaging are coupled with signal processing theory and methods, such as sampling theory, system identification, and spectral estimation, among others. Through this exposition, we hope to establish that ToF sensors are more than just depth sensors; depth information may be used to encode other forms of physical parameters, such as, the fluorescence lifetime of a biosample or the diffusion coefficient of turbid/scattering medium. The MATLAB scripts and ToF sensor data used for reproducing figures in this article are available via the author?s webpage: http://www.mit.edu/~ayush/Code.
Feigin M, Bhandari A, Izadi S, et al., 2016, Resolving Multipath Interference in Kinect: An Inverse Problem Approach, IEEE SENSORS JOURNAL, Vol: 16, Pages: 3419-3427, ISSN: 1530-437X
Bhandari A, Eldar YC, 2016, A swiss army knife for finite rate of innovation sampling theory, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Publisher: IEEE
Bhandari A, Wallace AM, Raskar R, 2016, Super-resolved time-of-flight sensing via FRI sampling theory, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Publisher: IEEE
Bhandari A, Barsi C, Raskar R, 2015, Blind and reference-free fluorescence lifetime estimation via consumer time-of-flight sensors, Optica, Vol: 2, Pages: 965-973, ISSN: 2334-2536
Fluorescence lifetime imaging (FLI) is a popular method for extracting useful information that is otherwise unavailable from a conventional intensity image. Usually, however, it requires expensive equipment, is often limited to either distinctly frequency- or time-domain modalities, and demands calibration measurements and precise knowledge of the illumination signal. Here, we present a generalized time-based, cost-effective method for estimating lifetimes by repurposing a consumer-grade time-of-flight sensor. By developing mathematical theory that unifies time- and frequency-domain approaches, we can interpret a time-based signal as a combination of multiple frequency measurements. We show that we can estimate lifetimes without knowledge of the illumination signal and without any calibration. We experimentally demonstrate this blind, reference-free method using a quantum dot solution and discuss the method’s implementation in FLI applications.
Feigin M, Whyte R, Bhandari A, et al., 2015, Modeling "wiggling" as a multi-path interference problem in AMCW ToF imaging, OPTICS EXPRESS, Vol: 23, Pages: 19213-19225, ISSN: 1094-4087
Bhandari A, Eldar YC, Raskar R, 2015, SUPER-RESOLUTION IN PHASE SPACE, 40th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Publisher: IEEE, Pages: 4155-4159, ISSN: 1520-6149
Bhandari A, Feigin M, Izadi S, et al., 2014, Resolving multipath interference in Kinect: An inverse problem approach, 2014 IEEE Sensors, Publisher: IEEE
Bhandari A, Kadambi A, Whyte R, et al., 2014, Resolving multipath interference in time-of-flight imaging via modulation frequency diversity and sparse regularization, Optics Letters, Vol: 39, Pages: 1705-1708, ISSN: 0146-9592
Time-of-flight (ToF) cameras calculate depth maps by reconstructing phase shifts of amplitude-modulated signals. For broad illumination of transparent objects, reflections from multiple scene points can illuminate a given pixel, giving rise to an erroneous depth map. We report here a sparsity-regularized solution that separates interfering components using multiple modulation frequency measurements. The method maps ToF imaging to the general framework of spectral estimation theory and has applications in improving depth profiles and exploiting multiple scattering.
Bhandari A, Kadambi A, Raskar R, 2014, SPARSE LINEAR OPERATOR IDENTIFICATION WITHOUT SPARSE REGULARIZATION ? APPLICATIONS TO MIXED PIXEL PROBLEM IN TIME-OF-FLIGHT/RANGE IMAGING, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Publisher: IEEE, ISSN: 1520-6149
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