{"title":"Sufficient Support Information to Ensure a Unique Solution to the Phase Problem","authors":"B. Brames","doi":"10.1364/srs.1986.thc2","DOIUrl":"https://doi.org/10.1364/srs.1986.thc2","url":null,"abstract":"It is evident that the support of a function can have a strong influence upon one’s ability to uniquely reconstruct that function from its autocorrelation, both in terms of solution multiplicity, and in the convergence of certain reconstruction algorithms. Greenaway [1] first demonstrated that the number of solutions to the one—dimensional phase problem is reduced if an internal region of the function in question is known to be zero. This is a strong statement, because generally the one-dimensional phase problem is intractable due to large numbers of non-equivalent solutions. More recently Sault [2] has shown that one can always ensure solution uniqueness for discrete functions if the internal zero region is specified and somewhat more complex.","PeriodicalId":262149,"journal":{"name":"Topical Meeting On Signal Recovery and Synthesis II","volume":"44 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":"116311783","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":"An Iterative Deconvolution Algorithm with Exponential Convergence","authors":"C. E. Morris, M. A. Richards, M. Hayes","doi":"10.1364/srs.1986.fb2","DOIUrl":"https://doi.org/10.1364/srs.1986.fb2","url":null,"abstract":"Iterative deconvolution is an established technique for recovering the input sequence of a linear shift-invariant system given the output sequence and some knowledge about the distorting system [1]. Since the standard approach to iterative deconvolution has a linear convergence rate, some authors have proposed techniques such as gradient search methods [2,3] and kernel splitting [4] to increase the rate of convergence. These methods, however, are either computationally expensive or do not achieve a substantial gain in convergence rate. In this paper we describe an accelerated iterative algorithm that requires slightly more computational time or memory storage than the standard approach while achieving a favorable exponential rate of convergence.","PeriodicalId":262149,"journal":{"name":"Topical Meeting On Signal Recovery and Synthesis II","volume":"39 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":"123353877","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":"Reconstruction of Axisymmetric Objects from One Silhouette","authors":"Patrick Van Hove","doi":"10.1364/srs.1986.thd3","DOIUrl":"https://doi.org/10.1364/srs.1986.thd3","url":null,"abstract":"Silhouettes of opaque convex objects in orthographic projections were studied in an earlier paper, using a representation on the Gaussian Sphere [1]. A similar argument is applied here to solve for the direct and inverse relations between axisymmetric objects and their silhouettes. Furthermore, a new method for determining object orientation in three dimensions is proposed for such objects, using our analysis of silhouette curvature [1]. Axisymmetric objects are completely determined by a section through their axis of symmetry, which we refer to as the object generator; their silhouettes are symmetric curves in the projection plane. The projection of the object into its silhouette reduces to a transformation between the object generator and the silhouette, which are both planar curves. This paper investigates the conditions under which inversion of this transformation is possible; see Fig. 1. Two cases arise, depending on whether or not the tilt is known between the axis of the object and the projection plane. The derivations summarized here apply to a large class of axisymmetric objects, including non-convex objects. The presentation will be accompanied by a large number of computer generated examples which illustrate various aspects of the theories we developed.","PeriodicalId":262149,"journal":{"name":"Topical Meeting On Signal Recovery and Synthesis II","volume":"55 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":"123015533","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":"Recognition of 3-D Objects from Partial View Data","authors":"Ronald Wu, H. Stark","doi":"10.1364/srs.1986.thd2","DOIUrl":"https://doi.org/10.1364/srs.1986.thd2","url":null,"abstract":"We consider a problem that occurs in machine vision research, namely, how to determine the class membership of an object when only partial view data about it is available. For example, suppose that a machine vision system must determine whether a physical (i.e., a three-dimensional) object belongs to class A or class B and only 90 degree view data is available. How should the data be organized into a useful feature vector? What rule should be used to determine class—membership? One way to proceed is via image recovery i.e., the restoration of missing view data using any of the several extrapolation algorithms known to the image recovery community. However if only class membership is desired, is image recovery really needed? First we note that if the partial view data is insufficient i.e, it contains no information that is not common to both classes, then image recovery will not work (now for that matter will anything else!). Second, assuming that the data is sufficient i.e., that it contains at least some data characteristic of only one class, image recovery may not be the answer for two reasons: 1) the recovery process is most-often ill-posed, thereby introducing possibly too much noise for subsequent discrimination; and 2) regularization may induce sufficient smoothing to destroy what little class-differentiability may exist in the partial data. Thus we concentrate on information recovery rather than image recovery. We are therefore led to the following problem statement: given partial view data of a 3-D object known to belong to one of M well-defined classes, what operation (linear or non-linear) will enhance the discriminating value of the data? The algorithm we have derived is based on the ful1-view algorithm described below.","PeriodicalId":262149,"journal":{"name":"Topical Meeting On Signal Recovery and Synthesis II","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":"115399493","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":"The Use of Singular Systems in Inverse Problems in Signal Processing","authors":"E. Pike, M. Bertero, C. De Mol","doi":"10.1364/srs.1986.fa2","DOIUrl":"https://doi.org/10.1364/srs.1986.fa2","url":null,"abstract":"In a number of experiments in various scientific fields a common method for determining certain characteristics of a physical sample is to observe the interaction between the sample and the radiation emitted by a known source. One or several detectors measure space and/or time variations of the scattered radiation, as scattering amplitudes, field fluctuations, absorption coefficients and so on. The output of the detectors can be digitized and the final result of the experiment is a set of (real or complex) numbers \u0000{gn}nN=1 stored in a computer. The interpretation of the data requires the solution of a mathematical problem, ie the restoration of the unknown characteristic of the sample from the set of numbers gn.","PeriodicalId":262149,"journal":{"name":"Topical Meeting On Signal Recovery and Synthesis II","volume":"1 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":"125799960","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}