Chin-Tu Chen, V. Johnson, W. H. Wong, Xiaoping Hub, C. Metz
{"title":"Statistical Methods for Image Restoration and Image Reconstruction","authors":"Chin-Tu Chen, V. Johnson, W. H. Wong, Xiaoping Hub, C. Metz","doi":"10.1364/srs.1989.wd1","DOIUrl":"https://doi.org/10.1364/srs.1989.wd1","url":null,"abstract":"This paper offers a general review of the application of statistical methods, including both maximum likelihood and Bayesian estimators, to problems in image restoration and image reconstruction.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128512539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical Investigation of Phase Retrieval Uniqueness","authors":"J. H. Seldin, J. Fienup","doi":"10.1364/srs.1989.fa2","DOIUrl":"https://doi.org/10.1364/srs.1989.fa2","url":null,"abstract":"The uniqueness of phase retrieval has been explored from a theoretical standpoint via the factorability of polynomials. The Fourier transform of a function (an image), f, sampled on a regular grid is a polynomial, F. Bruck and Sodin [1] have shown that if f can be written as the convolution of K non-Hermitian functions (equivalent to K irreducible polynomial factors in Fourier space), then there exist 2K-1 ambiguous solutions to the phase retrieval problem of reconstructing f from IFI. It is well known for the two-dimensional case that polynomials of two complex variables have probability zero of being factorable [1-3]. It has also been shown from a theoretical standpoint that the uniqueness condition is not sensitive to noise [4]. However, this does not answer the practical question: what is the likelihood of significant ambiguity when IFI is corrupted by a given level of noise? We approached this question by trying to determine, given an arbitrary image and its Fourier polynomial, how close is the nearest factorable polynomial, and does it have an ambiguous solution that is significantly different from the given polynomial? This paper explores this question for the case of images defined within a 3x2 support. A derivation of object-domain conditions for factorability provides a means for finding nearest factorable polynomials through a constrained minimization search over the space of 3x2 ambiguous images. These searches are implemented with different object-domain constraints in a Monte Carlo simulation to estimate the probability that the nearest factorable polynomial, with an ambiguous solution that is significantly different from a given image, is within some distance of the given polynomial.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117077812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Synthesis of a Holographic Beamformer Using a Separability Constraint","authors":"M. Eismann, A. Tai, J. Cederquist","doi":"10.1364/srs.1989.thc3","DOIUrl":"https://doi.org/10.1364/srs.1989.thc3","url":null,"abstract":"In applications such as laser radar, active coherent imaging (possibly using phase retrieval), and optical data processing, it is often desired to uniformly illuminate a rectangular area that is in the far-field of the source. When using a laser with a Gaussian (TEMoo) intensity distribution as a source, an optical device is required to modify the near-field complex amplitude distribution of the beam such that its phase and intensity become uniform upon propagation to the far-field. We investigated the use of a holographic system to efficiently redistribute the beam energy into a near-field sinc(x) sinc(y) complex amplitude distribution. This holographic system was synthesized using the Gerchberg-Saxton algorithm.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114664304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multiple Source Localization Via Redundancy Exploitation With Geometrically Redundant Planar Sensor Arrays","authors":"D. Stavrinides, M. Zoltowski","doi":"10.1364/srs.1989.thb3","DOIUrl":"https://doi.org/10.1364/srs.1989.thb3","url":null,"abstract":"A new scheme for estimating the respective radial directions of multiple radiating sources is introduced. The main contribution is the incorporation of a technique referred to as \"Pseudo Forward Backward averaging\" which judiciously exploits the inherent redundancy in a planar sensor array exhibiting the ESPRIT structure [2]. ESPRIT is a recently proposed bearing estimation algorithm that works with an array of M matched sensor pairs (2M sensors total) referred to as doublets, grouping one element of each doublet into an X array, and the other into a Y array. The displacement vector, denoted \u0000d→, between the two members of a given doublet is assumed to be the same for each doublet and the two members of each doublet are required to possess identical radiation patterns. ESPRIT allows us to estimate the angle between \u0000d→ and the unit normal to the i-th arriving wavefront, denoted by \u0000r^\u0000 i\u0000 , i.e., \u0000d→⋅r^\u0000 i\u0000 . In contrast to spatial spectrum estimation algorithms such as MUSIC and Maximum Entropy which require the plotting and searching of a multi-modal, two dimensional surface, the estimates obtained via ESPRIT are simply found by solving for the generalized eigenvalues of a judiciously formed data pencil. More specifically, we shall employ a refinement of ESPRIT, referred to as PRO-ESPRIT [1], the development of which was predicated on exploiting the inherent redundancy built into the ESPRIT array structure described above.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114583697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantitative Comparisons of Choices of Prior Information in Image Reconstruction","authors":"T. A. Gooley, H. Barrett, M. Barth, J. Denny","doi":"10.1364/srs.1989.wa3","DOIUrl":"https://doi.org/10.1364/srs.1989.wa3","url":null,"abstract":"Medical image reconstruction is fraught with problems that are a result of noisy and incomplete data. The incomplete data give rise to null functions that are associated with the imaging operator, thus yielding an infinite number of solutions that fit the data equally well. Noise in the data often will lead to very rough reconstructions, which can be inconsistent with previous experience. The use of prior information can sometimes be introduced to help alleviate the aforementioned problems. If one knows that an object (or class of objects) possesses certain characteristics, then the reconstructions should possess the same characteristics.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128018248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Direct Phase Estimation from Phase Differences Using Fast Elliptic PDE Solvers","authors":"D. Ghiglia, L. Romero","doi":"10.1364/srs.1989.fc2","DOIUrl":"https://doi.org/10.1364/srs.1989.fc2","url":null,"abstract":"Obtaining robust phase estimates from phase differences is a problem common to severed areas of importance to the optics and signal processing community. Specific areas of application include speckle imaging and interferometry, adaptive optics, compensated imaging, and coherent imaging such as synthetic-aperture radar. The purpose of this paper is to relate the equations describing the phase estimation problem to the general form of elliptic partial differential equations, and illustrate results of reconstructions on large M by N grids using existing, published, and readily available Fortran subroutines.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134106866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Phase Retrieval Using Two Fourier Intensities","authors":"Wooshik Kim, M. Hayes","doi":"10.1364/srs.1989.fb2","DOIUrl":"https://doi.org/10.1364/srs.1989.fb2","url":null,"abstract":"The two-dimensional discrete phase-retrieval problem is concerned with the reconstruction of a signal, or image, x(m, n), from the magnitude (intensity) of its Fourier transform, |X(ω1,ω2)|- Phase retrieval is an important problem that arises in a variety of different applications including x-ray crystallography, astronomy, electron microscopy, optics, and signal processing [1-5]. There are three issues that need to be considered in the solution of the phase retrieval problem: the uniqueness of the solution, the development of phase retrieval algorithms that reconstruct a signal from its Fourier transform intensity and any á priori information that might be available, and the sensitivity of the reconstruction to computational noise and measurements errors. It is now well known that if a two-dimensional signal with finite support has a z-transform that is an irreducible polynomial then the signal is uniquely defined to within a trivial ambiguity by the intensity of its Fourier transform [6]. This result becomes important with the fact that it has been shown that “almost all” discrete two-dimensional signals with finite support have z-transforms that are irreducible [7]. In spite of this uniqueness of the solution, however, the reconstruction of a signal from its Fourier intensity remains a difficult problem.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121799545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Local Criteria : A Unified Approach to Locally Adaptive Linear and Rank Filters","authors":"L. Yaroslavsky","doi":"10.1364/srs.1989.thb4","DOIUrl":"https://doi.org/10.1364/srs.1989.thb4","url":null,"abstract":"During the last several years a lot of new linear and nonlinear rank algorithms for signal and picture processing have been proposed [1-13]. The linear ones have been derived from one or another statistical model of the signal to be processed. The rank ones have been substantiated from different positions and without any rather general notion of optimality. The aim of this paper is to introduce a new family of criteria of processing quality as a basis for unified approach to synthesis of optimal linear and rank filters for signal and picture processing.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121837559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Superresolution with an Opacity Constraint","authors":"R. Paxman","doi":"10.1364/srs.1989.pd1","DOIUrl":"https://doi.org/10.1364/srs.1989.pd1","url":null,"abstract":"The term superresolution can be defined as the use of a priori information to achieve resolution superior to the diffraction-limited resolution. In this paper we explore the use of a novel type of prior knowledge in the context of 3-D imaging. We wish to exploit knowledge that the object being imaged is confined to a 2-D manifold (surface) embedded in a 3-D space. Such prior knowledge is valid when the object is opaque to the illuminating radiation so that only secondary sources that lie in the outer surface of the object contribute to the reflected field.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125858030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"3-D Tomographic Image Reconstruction from Incomplete Cone Beam Projections","authors":"H. Kudo, Tsuneo Saito","doi":"10.1364/srs.1989.fd2","DOIUrl":"https://doi.org/10.1364/srs.1989.fd2","url":null,"abstract":"3-D cone beam tomographic imaging system has attracted much attentions for its rapid data acquisition and high resolution image. Some attempts for its realization have been made, but many unsolved problems concerning its image reconstruction remain. In the typical 3-D cone beam tomography, an x-ray source moves on a bounded curve surrounding an object and a 2-D projection is recorded by the planar detector at each source position. For this geometry, the following informative theorem can be proved [1,2].","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114462644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}