Journal ArticleDOI
Image recovery from correlations
TLDR
In this article, an iterative technique for recovering images from measurements of nth-order correlations is proposed, which preserves nonnegativity, allows for the inclusion of known support constraints, and produces a sequence of images whose nthorder correlations better approximate the measured data as the iterations proceed.Abstract:
Many image-recovery problems involve the determination of a real-valued, nonnegative image whose nth-order correlation approximates some measured or specified function. Special cases are image recovery from second-order correlations, or phase retrieval, and image recovery from third-order correlations, or triple-correlation recovery. Examples include astronomical speckle imaging, spectroscopy, imaging correlography, and the measurement of ultrashort laser pulses. We propose an iterative technique for recovering images from measurements of nth-order correlations. This technique is shown to preserve nonnegativity, allow for the inclusion of known support constraints, and produce a sequence of images whose nth-order correlations better approximate the measured data as the iterations proceed.read more
Citations
More filters
Journal ArticleDOI
Deblurring subject to nonnegativity constraints
TL;DR: It is shown that every function in the sequence is nonnegative and the sequence converges monotonically to a global minimum.
Journal ArticleDOI
Information-theoretic image formation
TL;DR: The possible role of information theory in problems of image formation is to provide a rigorous framework for defining the imaging problem, for defining measures of optimality used to form estimates of images, for addressing issues associated with the development of algorithms based on these optimality criteria, and for quantifying the quality of the approximations.
Journal ArticleDOI
Deep iterative reconstruction for phase retrieval.
TL;DR: This work develops a phase retrieval algorithm that utilizes two DNNs together with the model-based HIO method that not only achieves state-of-the-art reconstruction performance but also is more robust to different initialization and noise levels.
Journal ArticleDOI
Stellar intensity interferometry: Prospects for sub-milliarcsecond optical imaging
TL;DR: In this paper, the authors present a survey of the possibilities of using an array of air Cherenkov telescopes at short wavelengths to obtain high-resolution images of rapidly rotating hot stars.
Journal ArticleDOI
Signal-processing approaches for image-resolution restoration for TOMBO imagery
Kerkil Choi,Timothy J. Schulz +1 more
TL;DR: This work constructs a computational data model based on Fourier optics and proposes restoration algorithms based on minimization of an information-theoretic measure, called Csiszár's I divergence, which can produce very high-quality estimates from noiseless measurements and reasonably good estimates from noisy measurements, even when the measurements are incomplete.
References
More filters
Journal ArticleDOI
Phase retrieval algorithms: a comparison.
TL;DR: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods and it is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm forThe problem of two intensity measurements converge.
Journal ArticleDOI
Maximum Likelihood Reconstruction for Emission Tomography
L. A. Shepp,Y. Vardi +1 more
TL;DR: In this paper, the authors proposed a more accurate general mathematical model for ET where an unknown emission density generates, and is to be reconstructed from, the number of counts n*(d) in each of D detector units d. Within the model, they gave an algorithm for determining an estimate? of? which maximizes the probability p(n*|?) of observing the actual detector count data n* over all possible densities?.
Journal Article
EM reconstruction algorithms for emission and transmission tomography.
Kenneth Lange,Richard E. Carson +1 more
TL;DR: The general principles behind all EM algorithms are discussed and in detail the specific algorithms for emission and transmission tomography are derived and the specification of necessary physical features such as source and detector geometries are discussed.
Journal ArticleDOI
Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy
John E. Shore,R. Johnson +1 more
TL;DR: Jaynes's principle of maximum entropy and Kullbacks principle of minimum cross-entropy (minimum directed divergence) are shown to be uniquely correct methods for inductive inference when new information is given in the form of expected values.
Journal ArticleDOI
Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems
TL;DR: In this article, logically consistent rules for selecting a vector from any feasible set defined by linear constraints, when either all $n$-vectors or those with positive components or the probability vectors are permissible, are determined.