Penalized-likelihood image reconstruction for digital holography.
01 May 2004-Journal of The Optical Society of America A-optics Image Science and Vision (Optical Society of America)-Vol. 21, Iss: 5, pp 737-750
TL;DR: A new numerical reconstruction approach using a statistical technique that reconstructs the complex field of the object from the real-valued hologram intensity data and derives an optimization transfer algorithm that monotonically decreases the cost function at each iteration.
Abstract: Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.
Citations
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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
TL;DR: A new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera that is sufficiently general to be applied to sophisticated optical setups that include a microscope objective.
Abstract: We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data sets and demonstrate its applicability to real-world experimental conditions by reconstructing optically acquired holograms.
217 citations
TL;DR: A broad discussion about the noise issue in DH is provided, with the aim of covering the best-performing noise reduction approaches that have been proposed so far and quantitative comparisons among these approaches will be presented.
Abstract: Digital holography (DH) has emerged as one of the most effective coherent imaging technologies. The technological developments of digital sensors and optical elements have made DH the primary approach in several research fields, from quantitative phase imaging to optical metrology and 3D display technologies, to name a few. Like many other digital imaging techniques, DH must cope with the issue of speckle artifacts, due to the coherent nature of the required light sources. Despite the complexity of the recently proposed de-speckling methods, many have not yet attained the required level of effectiveness. That is, a universal denoising strategy for completely suppressing holographic noise has not yet been established. Thus the removal of speckle noise from holographic images represents a bottleneck for the entire optics and photonics scientific community. This review article provides a broad discussion about the noise issue in DH, with the aim of covering the best-performing noise reduction approaches that have been proposed so far. Quantitative comparisons among these approaches will be presented.
176 citations
TL;DR: This Letter suggests the use of a sparsity-promoting prior, verified in many inline holography applications, and presents a simple iterative algorithm for 3D object reconstruction under sparsity and positivity constraints.
Abstract: Inline digital holograms are classically reconstructed using linear operators to model diffraction. It has long been recognized that such reconstruction operators do not invert the hologram formation operator. Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin images. When objects located at different depths are reconstructed from a hologram, in-focus and out-of-focus images of all objects superimpose upon each other. Additional processing, such as maximum-of-focus detection, is thus unavoidable for any successful use of the reconstructed volume. In this Letter, we consider inverting the hologram formation model in a Bayesian framework. We suggest the use of a sparsity-promoting prior, verified in many inline holography applications, and present a simple iterative algorithm for 3D object reconstruction under sparsity and positivity constraints. Preliminary results with both simulated and experimental holograms are highly promising.
163 citations
TL;DR: In this article, the authors proposed a microparticle localization scheme in digital holography based on the inverse-problems approach, which yields the optimal particle set that best models the observed hologram image and resolves this global optimization problem by conventional particle detection followed by a local refinement for each particle.
Abstract: We propose a microparticle localization scheme in digital holography Most conventional digital holography methods are based on Fresnel transform and present several problems such as twin-image noise, border effects, and other effects To avoid these difficulties, we propose an inverse-problem approach, which yields the optimal particle set that best models the observed hologram image We resolve this global optimization problem by conventional particle detection followed by a local refinement for each particle Results for both simulated and real digital holograms show strong improvement in the localization of the particles, particularly along the depth dimension In our simulations, the position precision is > or =1 microm rms Our results also show that the localization precision does not deteriorate for particles near the edge of the field of view
157 citations
References
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TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.
Abstract: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968. All material has been thoroughly updated and several new sections explore recent progress in important areas, such as wavelength modulation, analog information processing, and holography. Fourier analysis is a ubiquitous tool with applications in diverse areas of physics and engineering. This book explores these applications in the field of optics with a special emphasis on applications to diffraction, imaging, optical data processing, and holography. This book can be used as a textbook to satisfy the needs of several different types of courses, and it is directed toward both engineers ad physicists. By varying the emphasis on different topics and specific applications, the book can be used successfully in a wide range of basic Fourier Optics or Optical Signal Processing courses.
12,159 citations
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"Penalized-likelihood image reconstr..." refers methods in this paper
...(18) Instead of using the condition above, we choose a surrogate function f(x; xn) that satisfies the following sufficient conditions:...
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TL;DR: An improvement of the resolution by one decimal wotild require a correction of the objective to four decimals, a practically hopeless task.
Abstract: IT is known that the spherical aberration of electron lenses sets a limit to the resolving power of electron microscopes at about 5 A. Suggestions for the correction of objectives have been made ; but these are difficult in themselves, and the prospects of improvement are further aggravated by the fact that the resolution limit is proportional to the fourth root of the spherical aberration. Tnus an improvement of the resolution by one decimal wotild require a correction of the objective to four decimals, a practically hopeless task.
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"Penalized-likelihood image reconstr..." refers background or methods in this paper
...Unlike the conventional filtering method, iterative techniques can use all of the information in the model (2) rather than discarding all but one of the four terms....
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...(2) and taking the Fourier transform, we convert the spatial-frequency spectrum of the recorded interference pattern into an angular spectrum of diffracted waves: I~n! 5 Io~n! 1 uUrefu(2)d ~n! 1 Uref Uo~n 2 a!...
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...(2) constitute the zero-order image; the third term, which is proportional to uo , leads to the formation of the primary image; and the fourth term, which is proportional to uo* , leads to the formation of the conjugate image....
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...5 uuo~r!u(2) 1 uuref~r!u(2) 1 uo~r!uref * ~r! 1 uo* ~r!uref~r!, (2)...
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