Binary Compressed Imaging

Bourquard, Aurélien; Unser, Michaël

doi:10.1109/tip.2012.2226900

Cited by 19 publications

(28 citation statements)

References 33 publications

(91 reference statements)

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“…Note that, while this optimum only represents an ideal solution (for some arguably acceptable noise-level range) in the framework of a particular acquisition and (algorithmic) reconstruction setting, we found experimentally that it also allowed to obtain satisfactory results when considering other CS approaches than the one of [15]. In that sense, even though the analysis we performed is specific, the trend as a function of the amount of impulses may be a general one (that one may re-investigate using Cramer-Rao bounds or similar).…”

Section: Discussionmentioning

confidence: 84%

“…Accordingly, we propose to study the behavior of the reconstruction quality as a function of the amount of impulses in the framework of 1-bit CS. More specifically, we consider the optical CS framework proposed in [15] where pixels are acquired as compressed binary values. While that work tackles the noiseless case, we study the behavior of the reconstruction with distinct amounts of additive Gaussian noise on the acquisition side (the noise being a cause of degradation of the measurements and thus of the reconstructed object profile).…”

Section: Discussionmentioning

confidence: 99%

“…While that work tackles the noiseless case, we study the behavior of the reconstruction with distinct amounts of additive Gaussian noise on the acquisition side (the noise being a cause of degradation of the measurements and thus of the reconstructed object profile). The noise parameter s is defined as the ratio between the noise standard deviation and the maximum noiseless image intensity (the noise being applied before the finite differentiation and binarization operations described in [15]). Results are shown in Fig.…”

Section: Discussionmentioning

confidence: 99%

“…1. The effect of our convolution based model on the object x can be described as a 4F-type system [7,15,16]. Following the direction d of light propagation, the input light intensities are transformed into the image y = (x ⇤ h), the latter being captured by a sensor array.…”

Section: Proposed Optical Modelmentioning

confidence: 99%

“…While the {0, p} set of phases captures all zero-crossings of the real part of the complexexponential sum in m, it remains insensitive to all imaginary components. This amounts to discarding the latter, thus creating additional conjugate complex exponentials-each of which corresponds to the addition of a symmetric impulse-to the original mask profile unless they are already present in the original mask profile m. Our PSF has to comply with two essential yet competing properties: (1) measurement pseudo-randomness [15] and (2) minimal measurement SNR. On the one hand, as a necessary condition, measurement pseudo-randomness requires the PSF to be composed of enough pseudo-randomly scattered impulses spread over a large enough FOV, so that every single measurement combines information of several unknowns [20].…”

Section: Phase-only Approximationmentioning

confidence: 99%

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Compressed imaging by sparse random convolution

Marcos¹,

Lasser²,

López³

et al. 2016

Opt. Express

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The theory of compressed sensing (CS) shows that signals can be acquired at sub-Nyquist rates if they are sufficiently sparse or compressible. Since many images bear this property, several acquisition models have been proposed for optical CS. An interesting approach is random convolution (RC). In contrast with single-pixel CS approaches, RC allows for the parallel capture of visual information on a sensor array as in conventional imaging approaches. Unfortunately, the RC strategy is difficult to implement as is in practical settings due to important contrast-to-noise-ratio (CNR) limitations. In this paper, we introduce a modified RC model circumventing such difficulties by considering measurement matrices involving sparse non-negative entries. We then implement this model based on a slightly modified microscopy setup using incoherent light. Our experiments demonstrate the suitability of this approach for dealing with distinct CS scenarii, including 1-bit CS. Abstract:The theory of compressed sensing (CS) shows that signals can be acquired at sub-Nyquist rates if they are sufficiently sparse or compressible. Since many images bear this property, several acquisition models have been proposed for optical CS. An interesting approach is random convolution (RC). In contrast with single-pixel CS approaches, RC allows for the parallel capture of visual information on a sensor array as in conventional imaging approaches. Unfortunately, the RC strategy is difficult to implement as is in practical settings due to important contrastto-noise-ratio (CNR) limitations. In this paper, we introduce a modified RC model circumventing such difficulties by considering measurement matrices involving sparse non-negative entries. We then implement this model based on a slightly modified microscopy setup using incoherent light. Our experiments demonstrate the suitability of this approach for dealing with distinct CS scenarii, including 1-bit CS.

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Section: Discussionmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Proposed Optical Modelmentioning

confidence: 99%

Section: Phase-only Approximationmentioning

confidence: 99%

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Compressed imaging by sparse random convolution

Marcos¹,

Lasser²,

López³

et al. 2016

Opt. Express

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Recovery error bounds on compressed sensing of noisy signals

Rateb

Yusof

2013

Int J Communication

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SUMMARYCompressed sensing is an emerging technique in the field of digital signal acquisition. It promises almost exact recovery of high-dimensional signals from a very small set of measurements. However, this technique is challenged by the task of recovering signals immersed in noise. In this paper, we derive upper and lower bounds on mean squared recovery error of noisy signals. These bounds are valid for any number of acquired measurements and at any signal-to-noise ratio. This work is highly useful for the design of any compressed sensing-based real world application by quantifying recovery error entailed with realistic digital signal acquisition scenarios.

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Compressed sampling reconstruction of hyperspectral images based on spectral prediction

Wang

Feng

2015

IEEJ Transactions Elec Engng

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With increasing amounts of hyperspectral images (HSI) and the limitations of the memory requirements, compressive techniques for hyperspectral images have attracted extensive research efforts in recent years. The main difficulty of applying compressed sampling (CS) theory to compression and reconstruction of hyperspectral images lies in using the spatial correlation and spectral correlation of hyperspectral images. In this paper, a reconstruction algorithm of hyperspectral images taking advantage of two‐dimensional compressed sampling (2DCS) and two‐dimensional total variation (2DTV) incorporating spectral prediction (SP) is investigated. In the sampling process, the hyperspectral images are divided into reference bands and common bands, and all bands are sampled using 2DCS independently. In the reconstruction process, the reference bands are reconstructed by 2DTV first. In order to improve the reconstruction quality of common bands, spectral prediction utilizing the spectral correlation between reference bands and common bands is conducted. Then the spectral compensation is computed by using a combination of the prediction value and the initial approximation for the common bands. The residual between the compensation value and the original value is obtained to revise the approximation for the common bands. The algorithm is implemented in an iterative manner to enhance the performance. Experimental results on popular hyperspectral datasets reveal that the proposed algorithm exploiting spectral prediction outperforms the algorithm 2DCS‐2DTV, which does not use spectral correlation, as well as the state‐of‐the‐art algorithms in terms of peak signal‐to‐noise ratio (PSNR). In particular, when the sampling rate of the reference bands is higher than that of the common bands, the proposed algorithm would improve the reconstruction quality dramatically. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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Binary Compressed Imaging

Cited by 19 publications

References 33 publications

Compressed imaging by sparse random convolution

Compressed imaging by sparse random convolution

Recovery error bounds on compressed sensing of noisy signals

Compressed sampling reconstruction of hyperspectral images based on spectral prediction

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