Compressive correlation holography.
TL;DR: This study reveals that liminal CS requires far fewer samples for the reconstruction of the hologram and has wide application in image reconstruction.
Abstract: We propose and demonstrate a compressive sensing (CS) framework for correlation holography. This is accomplished by adopting the principle of compressive sensing and thresholding in the two-point intensity correlation. The measurement matrix and the sensing matrix that are required for applying the CS framework here are systematically extracted from the random illuminations of the laser speckle data. Reconstruction results using CS, CS with thresholding, and intensity correlation are compared. Our study reveals that liminal CS requires far fewer samples for the reconstruction of the hologram and has wide application in image reconstruction.
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TL;DR: It is established that an object can be recovered from limited size of a recorded hologram with the constraint that object has to be sparse in known basis and the finding highlights that the CS reconstruction is better than that of IFT reconstruction.
8 citations
TL;DR: Structured transmittance illumination coherence holography (STICH) as discussed by the authors reconstructs complex coherence from the intensity measurement in a single-pixel detector without an interferometric setup and also keeps advantages of the intensity correlations.
Abstract: The coherence holography offers an unconventional way to reconstruct the hologram where an incoherent light illumination is used for reconstruction purposes, and object encoded into the hologram is reconstructed as the distribution of the complex coherence function. Measurement of the coherence function usually requires an interferometric setup and array detectors. This paper presents an entirely new idea of reconstruction of the complex coherence function in the coherence holography without an interferometric setup. This is realized by structured pattern projections on the incoherent source structure and implementing measurement of the cross-covariance of the intensities by a single-pixel detector. This technique, named structured transmittance illumination coherence holography (STICH), helps to reconstruct the complex coherence from the intensity measurement in a single-pixel detector without an interferometric setup and also keeps advantages of the intensity correlations. A simple experimental setup is presented as a first step to realize the technique, and results based on the computer modeling of the experimental setup are presented to show validation of the idea.
4 citations
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TL;DR: This paper proposes gradient projection algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems and test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method.
Abstract: Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ) error term combined with a sparseness-inducing regularization term. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution, and compressed sensing are a few well-known examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems. We test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method. Computational experiments show that these GP approaches perform well in a wide range of applications, often being significantly faster (in terms of computation time) than competing methods. Although the performance of GP methods tends to degrade as the regularization term is de-emphasized, we show how they can be embedded in a continuation scheme to recover their efficient practical performance.
3,488 citations
01 Jan 2012
TL;DR: In this paper, the authors introduce the concept of second generation sparse modeling and apply it to the problem of compressed sensing of analog signals, and propose a greedy algorithm for compressed sensing with high-dimensional geometry.
Abstract: Machine generated contents note: 1. Introduction to compressed sensing Mark A. Davenport, Marco F. Duarte, Yonina C. Eldar and Gitta Kutyniok; 2. Second generation sparse modeling: structured and collaborative signal analysis Alexey Castrodad, Ignacio Ramirez, Guillermo Sapiro, Pablo Sprechmann and Guoshen Yu; 3. Xampling: compressed sensing of analog signals Moshe Mishali and Yonina C. Eldar; 4. Sampling at the rate of innovation: theory and applications Jose Antonia Uriguen, Yonina C. Eldar, Pier Luigi Dragotta and Zvika Ben-Haim; 5. Introduction to the non-asymptotic analysis of random matrices Roman Vershynin; 6. Adaptive sensing for sparse recovery Jarvis Haupt and Robert Nowak; 7. Fundamental thresholds in compressed sensing: a high-dimensional geometry approach Weiyu Xu and Babak Hassibi; 8. Greedy algorithms for compressed sensing Thomas Blumensath, Michael E. Davies and Gabriel Rilling; 9. Graphical models concepts in compressed sensing Andrea Montanari; 10. Finding needles in compressed haystacks Robert Calderbank, Sina Jafarpour and Jeremy Kent; 11. Data separation by sparse representations Gitta Kutyniok; 12. Face recognition by sparse representation Arvind Ganesh, Andrew Wagner, Zihan Zhou, Allen Y. Yang, Yi Ma and John Wright.
1,824 citations
TL;DR: In this article, a single high-resolution image of the scattered light, captured with a standard camera, encodes sufficient information to image through visually opaque layers and around corners with diffraction-limited resolution.
Abstract: Optical imaging through and inside complex samples is a difficult challenge with important applications in many fields. The fundamental problem is that inhomogeneous samples such as biological tissue randomly scatter and diffuse light, preventing the formation of diffraction-limited images. Despite many recent advances, no current method can perform non-invasive imaging in real-time using diffused light. Here, we show that, owing to the ‘memory-effect’ for speckle correlations, a single high-resolution image of the scattered light, captured with a standard camera, encodes sufficient information to image through visually opaque layers and around corners with diffraction-limited resolution. We experimentally demonstrate single-shot imaging through scattering media and around corners using spatially incoherent light and various samples, from white paint to dynamic biological samples. Our single-shot lensless technique is simple, does not require wavefront-shaping nor time-gated or interferometric detection, and is realized here using a camera-phone. It has the potential to enable imaging in currently inaccessible scenarios. Diffraction-limited imaging in a variety of complex media is realized based on analysis of speckle correlations in light captured using a camera phone.
899 citations
TL;DR: In this paper, an advanced image reconstruction algorithm for pseudothermal ghost imaging, based on compressed sensing, is presented. But the algorithm is limited to pseudothermal images and cannot be applied to images taken from other pseudothermal imaging experiments.
Abstract: We describe an advanced image reconstruction algorithm for pseudothermal ghost imaging, reducing the number of measurements required for image recovery by an order of magnitude. The algorithm is based on compressed sensing, a technique that enables the reconstruction of an N-pixel image from much less than N measurements. We demonstrate the algorithm using experimental data from a pseudothermal ghost-imaging setup. The algorithm can be applied to data taken from past pseudothermal ghost-imaging experiments, improving the reconstruction’s quality.
793 citations
TL;DR: In this paper, a scheme for coherent imaging that exploits the classical correlation of two beams obtained by splitting incoherent thermal radiation is considered, and a precise formal analogy is pointed out.
Abstract: We consider a scheme for coherent imaging that exploits the classical correlation of two beams obtained by splitting incoherent thermal radiation. This case is analyzed in parallel with the configuration based on two entangled beams produced by parametric down-conversion, and a precise formal analogy is pointed out. This analogy opens the possibility of using classical beams from thermal radiation for ghost imaging schemes in the same way as entangled beams.
734 citations