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Journal ArticleDOI

Compressive Fresnel Holography

TL;DR: This work demonstrates successful application of compressive sensing framework to digital Fresnel holography and it is shown that when applying compressed sensing approach to Fresnel fields a special sampling scheme should be adopted for improved results.
Abstract: Compressive sensing is a relatively new measurement paradigm which seeks to capture the “essential” aspects of a high-dimensional object using as few measurements as possible. In this work we demonstrate successful application of compressive sensing framework to digital Fresnel holography. It is shown that when applying compressive sensing approach to Fresnel fields a special sampling scheme should be adopted for improved results.
Citations
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Journal ArticleDOI
TL;DR: Unique features of lens-free computational imaging tools are discussed and some of their emerging results for wide-field on-chip microscopy, such as the achievement of a numerical aperture of ∼0.8–0.9 across a field of view (FOV) of more than 20 mm2, which corresponds to an image with more than 1.5 gigapixels.
Abstract: In this perspective, the authors present the basic features of lens-free computational imaging tools and report performance comparisons with conventional microscopy methods. They also discuss the challenges that these computational on-chip microscopes face for their wide-scale biomedical application.

486 citations

Journal ArticleDOI
20 Aug 2019
TL;DR: This paper relates the deep-learning-inspired solutions to the original computational imaging formulation and use the relationship to derive design insights, principles, and caveats of more general applicability, and explores how the machine learning process is aided by the physics of imaging when ill posedness and uncertainties become particularly severe.
Abstract: Since their inception in the 1930–1960s, the research disciplines of computational imaging and machine learning have followed parallel tracks and, during the last two decades, experienced explosive growth drawing on similar progress in mathematical optimization and computing hardware. While these developments have always been to the benefit of image interpretation and machine vision, only recently has it become evident that machine learning architectures, and deep neural networks in particular, can be effective for computational image formation, aside from interpretation. The deep learning approach has proven to be especially attractive when the measurement is noisy and the measurement operator ill posed or uncertain. Examples reviewed here are: super-resolution; lensless retrieval of phase and complex amplitude from intensity; photon-limited scenes, including ghost imaging; and imaging through scatter. In this paper, we cast these works in a common framework. We relate the deep-learning-inspired solutions to the original computational imaging formulation and use the relationship to derive design insights, principles, and caveats of more general applicability. We also explore how the machine learning process is aided by the physics of imaging when ill posedness and uncertainties become particularly severe. It is hoped that the present unifying exposition will stimulate further progress in this promising field of research.

473 citations

01 Jan 2012
TL;DR: This work demonstrates single frame 3D tomography from 2D holographic data using compressed sampling, which enables signal reconstruction using less than one measurement per reconstructed signal value.
Abstract: Compressive holography estimates images from incomplete data by using sparsity priors. Compressive holography combines digital holography and compressive sensing. Digital holography consists of computational image estimation from data captured by an electronic focal plane array. Compressive sensing enables accurate data reconstruction by prior knowledge on desired signal. Computational and optical co-design optimally supports compressive holography in the joint computational and optical domain. This dissertation explores two examples of compressive holography: estimation of 3D tomographic images from 2D data and estimation of images from under sampled apertures. Compressive holography achieves single shot holographic tomography using decompressive inference. In general, 3D image reconstruction suffers from underdetermined measurements with a 2D detector. Specifically, single shot holographic tomography shows the uniqueness problem in the axial direction because the inversion is ill-posed. Compressive sensing alleviates the ill-posed problem by enforcing some sparsity constraints. Holographic tomography is applied for video-rate microscopic imaging and diffuse object imaging. In diffuse object imaging, sparsity priors are not valid in coherent image basis due to speckle. So incoherent image estimation is designed to hold the sparsity in incoherent image basis by support of multiple speckle realizations. High pixel count holography achieves high resolution and wide field-of-view imaging. Coherent aperture synthesis can be one method to increase the aperture size of a detector. Scanning-based synthetic aperture confronts a multivariable global optimization problem due to time-space measurement errors. A hierarchical estimation strategy divides the global problem into multiple local problems with support of computational and optical co-design. Compressive sparse aperture holography can be another method. Compressive sparse sampling collects most of significant field information with a small fill factor because object scattered fields are locally redundant. Incoherent image estimation is adopted for the expanded modulation transfer function and compressive reconstruction.

310 citations

Journal ArticleDOI
TL;DR: It is demonstrated that it is possible to robustly and efficiently identify an unknown signal solely from phaseless Fourier measurements, a fact with potentially far-reaching implications.
Abstract: Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264Classic Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Recent Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266Sparse Phase Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273Phase Retrieval Using Masks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Uniqueness and Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275SDP Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Wirtinger Flow Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Combinatorial Methods (for the Noiseless Setting) . . . . . . . . . . . . . . . . 278Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 STFT Phase Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 Nonvanishing Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Sparse Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292Introduction In many physical measurement systems, one can only measure the power spectral density, that is, the magnitude square of the Fourier transform of the underlying signal. For example, in an optical setting, detection devices like CCD cameras and photosensitive films cannot measure the phase of a light wave and instead measure the photon flux. In addition, at a large enough distance from the imaging plane the field is given by the Fourier transform of the image (up to a known phase factor). Thus, in the far field, optical devices essentially measure the Fourier transform magnitude. Since the phase encodes a lot of the structural content of the image, important information is lost. The problem of reconstructing a signal from its Fourier magnitude is known as phase retrieval [1,2]. This reconstruction problem is one with a rich history and arises in many areas of engineering and applied physics, including optics [3], x-ray crystallography [4], astronomical imaging [5], speech processing [6], computational biology [7], and blind deconvolution [8].

207 citations


Cites background from "Compressive Fresnel Holography"

  • ...Recently, the use of sparsity has also become popular in optical applications including holography [65], super-resolution and sub-wavelength imaging [66–71] and ankylography [73,74]....

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01 Jan 2006
TL;DR: Digital holography is a technique that permits digital capture of holograms and subsequent processing on a digital computer as mentioned in this paper, and various applications of this technique cover three-dimensional (3-D) imaging as well as several problems.
Abstract: Digital holography is a technique that permits digital capture of holograms and subsequent processing on a digital computer. This paper reviews various applications of this technique. The presented applications cover three-dimensional (3-D) imaging as well as several associated problems. For the case of 3-D imaging, optical and digital methods to reconstruct and visualize the recorded objects are described. In addition, techniques to compress and encrypt 3-D information in the form of digital holograms are presented. Lastly, 3-D pattern recognition applications of digital holography are discussed. The described techniques constitute a comprehensive approach to 3-D imaging and processing.

179 citations

References
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Journal ArticleDOI
TL;DR: The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.
Abstract: Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use.

9,686 citations


"Compressive Fresnel Holography" refers background or methods or result in this paper

  • ...Our nonuniform (variable density) sampling scheme is described in Section IV....

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  • ...In order to describe CS, let us think of an object described by an -dimensional real valued vector (in case that the object Manuscript received December 03, 2009; revised January 26, 2010; accepted January 26, 2010....

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  • ...This is in contrast to most imaging applications where we only detect variations in the squared modulus of the propagating optical field....

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Journal ArticleDOI
TL;DR: It is shown that ‘1 minimization recovers x 0 exactly when the number of measurements exceeds m Const ·µ 2 (U) ·S · logn, where S is the numberof nonzero components in x 0, and µ is the largest entry in U properly normalized: µ(U) = p n · maxk,j |Uk,j|.
Abstract: We consider the problem of reconstructing a sparse signal x 0 2 R n from a limited number of linear measurements. Given m randomly selected samples of Ux 0 , where U is an orthonormal matrix, we show that ‘1 minimization recovers x 0 exactly when the number of measurements exceeds m Const ·µ 2 (U) ·S · logn, where S is the number of nonzero components in x 0 , and µ is the largest entry in U properly normalized: µ(U) = p n · maxk,j |Uk,j|. The smaller µ, the fewer samples needed. The result holds for “most” sparse signals x 0 supported on a fixed (but arbitrary) set T. Given T, if the sign of x 0 for each nonzero entry on T and the observed values of Ux 0 are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples.

2,187 citations


"Compressive Fresnel Holography" refers background or result in this paper

  • ...In order to describe CS, let us think of an object described by an -dimensional real valued vector (in case that the object Manuscript received December 03, 2009; revised January 26, 2010; accepted January 26, 2010....

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  • ...3(d) has the advantages of the low coherence of the Fourier-wavelet basis at coarse scales, where the signal tends to be less sparse, and the universality of the Gaussian random projections sensing [17] in fine scales, where the signal tends to be more sparse....

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  • ...This is in contrast to most imaging applications where we only detect variations in the squared modulus of the propagating optical field....

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  • ...This infers that more samples should be taken around the origin in order to take full advantage of the incoherence properties of the Fourier-wavelet transform....

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Journal ArticleDOI
TL;DR: A new method is proposed in which the distribution of complex amplitude at a plane is measured by phase-shifting interferometry and then Fresnel transformed by a digital computer, which can reconstruct an arbitrary cross section of a three-dimensional object with higher image quality and a wider viewing angle than from conventional digital holography using an off-axis configuration.
Abstract: A new method for three-dimensional image formation is proposed in which the distribution of complex amplitude at a plane is measured by phase-shifting interferometry and then Fresnel transformed by a digital computer. The method can reconstruct an arbitrary cross section of a three-dimensional object with higher image quality and a wider viewing angle than from conventional digital holography using an off-axis configuration. Basic principles and experimental verification are described.

1,813 citations

Journal ArticleDOI
TL;DR: A new application of digital holography for phase-contrast imaging and optical metrology and an application to surface profilometry shows excellent agreement with contact-stylus probe measurements.
Abstract: We present a new application of digital holography for phase-contrast imaging and optical metrology. This holographic imaging technique uses a CCD camera for recording of a digital Fresnel off-axis hologram and a numerical method for hologram reconstruction. The method simultaneously provides an amplitude-contrast image and a quantitative phase-contrast image. An application to surface profilometry is presented and shows excellent agreement with contact-stylus probe measurements.

1,202 citations

Journal ArticleDOI
TL;DR: A digital holographic technique is implemented in a microscope for three-dimensional imaging reconstruction using a Mach-Zehnder interferometer that uses an incoherent light source to remove the coherent noise that is inherent in the laser sources.
Abstract: A digital holographic technique is implemented in a microscope for three-dimensional imaging reconstruction. The setup is a Mach–Zehnder interferometer that uses an incoherent light source to remove the coherent noise that is inherent in the laser sources. A phase-stepping technique determines the optical phase in the image plane of the microscope. Out-of-focus planes are refocused by digital holographic computations, thus considerably enlarging the depth of investigation without the need to change the optical focus mechanically. The technique can be implemented in transmission for various magnification ratios and can cover a wide range of applications. Performances and limitations of the microscope are theoretically evaluated. Experimental results for a test target are given, and examples of two applications in particle localization and investigation of biological sample are provided.

368 citations


"Compressive Fresnel Holography" refers background in this paper

  • ...VARIABLE DENSITY SUB-SAMPLING OF THE FRESNEL TRANSFORM The motivation for the variable sampling density scheme appears evident from the examination of the effect of the Fresnel transform on the joint spatial-spatial frequency distribution (phase-space distribution) of the object field....

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