{"title":"Phase Retrieval for a Complex-Valued Object Using a Low-Resolution Image","authors":"J. Fienup, A. Kowalczyk","doi":"10.1364/JOSAA.7.000450","DOIUrl":"https://doi.org/10.1364/JOSAA.7.000450","url":null,"abstract":"Phase retrieval from a single Fourier intensity distribution is very difficult for complex valued objects unless the object has a support that is very well known, has a special type of support, or has strong glints [1-3]. In this paper we show that even the most difficult types of complex objects can be reconstructed if one has a very low-resolution intensity image of the object to supplement the Fourier intensity data.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116922924","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":"Complex submicrometric object retrieval in partially coherent microscopy","authors":"E. Lantz, J. Duvemoy","doi":"10.1364/srs.1989.wd2","DOIUrl":"https://doi.org/10.1364/srs.1989.wd2","url":null,"abstract":"This paper deals with the retrieval of an 1-d, space limited submicrometric complex object, from partially coherent images obtained by optical microscopy.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"72 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":"125877281","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":"Image Motion Recovery Using the Method of Total Least Squares","authors":"C. H. Chu, E. Delp","doi":"10.1364/srs.1989.tha1","DOIUrl":"https://doi.org/10.1364/srs.1989.tha1","url":null,"abstract":"Recovering image motion in the form of a velocity field is particularly useful in image analysis when the signal-to-noise ratio is low in individual frames of an image sequence. The velocity vector of a point on an image plane is the position change of the projection of an object point due to a change of viewing angle between the sensor and the object point. A change in the viewing angle can be caused by the velocity of the sensor, or the movement of the object point in the scene, or both. The velocity vector is thus an approximation to the velocity of the image point.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"117 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":"122638756","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":"Properties and Computational Implications of Zero-Sheets","authors":"R. Bates, B. K. Quek","doi":"10.1364/srs.1989.wc2","DOIUrl":"https://doi.org/10.1364/srs.1989.wc2","url":null,"abstract":"The spectrum (i.e. Fourier transform) of a K-dimensional compact (i.e. of finite amplitude and size) image is characterised (up to an arbitrary complex constant) by its zero-sheet, which is the (2K-2)-dimensional surface whereon the spectrum vanishes in 2K-dimensional complex Fourier space (constructed by generalising each real Fourier coordinate to a complex variable) [1].","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"36 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":"129750277","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 Error Correction by Shear Averaging","authors":"J. Fienup","doi":"10.1364/srs.1989.fb1","DOIUrl":"https://doi.org/10.1364/srs.1989.fb1","url":null,"abstract":"Synthetic aperture radar (SAR) [1,2] (and other imaging systems) measures the complex Fourier transform (called the signal history or phase history) of the scene being imaged, but it often suffers from one-dimensional (1-D) phase errors due to unknown system platform motion, target motion, system phase instabilities, and propagation through atmospheric turbulence. If uncorrected, these phase errors can cause severe blurring or smearing of the imagery. Phase errors (the residual phase errors remaining after correction for the measured motion) can be corrected by digital phase-error correction (sometimes called autofocus) methods, the most widely used being \"sub-aperture processing\" and \"prominent-point processing.\" The disadvantage of sub-aperture processing, which is analogous to the concept of a Hartmann sensor in optics, is that it only works for low-order (up to about fourth-order) polynomial-type phase errors. The disadvantage of prominent-point processing, which deconvolves an image based on an estimate of the impulse response of the system, is that it requires the presence of an identifiable, isolated, strong point-like reflector in the scene being imaged. Furthermore, both of these two processing methods require extensive computations.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"7 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":"121325462","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":"Experimental confirmation of superresolution in incoherent confocal scanning microscopy using a singular system inversion","authors":"M. R. Young, R. Davies, E. Pike, J. Walker","doi":"10.1364/srs.1989.wd4","DOIUrl":"https://doi.org/10.1364/srs.1989.wd4","url":null,"abstract":"Singular system inversion techniques provide the basis for processing data obtained from an array of N detectors in the image plane of a confocal scanning microscope system as proposed by Bertero and Pike [1]. For an infinite number of detectors, the theory (see companion paper) predicts a transfer function of the form Experimental confirmation is presented here for the case of a 1-D low-numerical-aperture incoherent system, an important result being that with as few as five detectors, spaced at half the (coherent-case) Rayleigh distance, R, a notable improvement over the conventional confocal scanning microscope system is achieved.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"50 7 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":"124358185","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":"Use of Fourier Domain Real Plane-Zeros in Phase Retrieval","authors":"C. Wackerman, A. Yagle","doi":"10.1364/srs.1989.fa4","DOIUrl":"https://doi.org/10.1364/srs.1989.fa4","url":null,"abstract":"Throughout a large number of disciplines, including astronomy, wave-front sensing and x-ray crystallography, there exists a class of problems referred to as the phase retrieval problem; given the modulus |F(u,v)| of the Fourier transform of an object f(x,y) and some constraints about the form of f(x,y), reconstruct f(x,y). Several solutions to this problem have been proposed, but our research has concentrated on the iterative Fourier transform algorithm (IFTA) [1,2] which has the advantages of being robust under noisy conditions and not computationally burdensome. An area of difficulty for the IFTA however is that the algorithm often stagnates at a reconstruction with stripe like noise, especially for real, non-negative objects [3]. This paper will present research that we have done to address this problem by using information about locations in the Fourier plane where F(u,v) is identically zero, what we will call Fourier domain real-plane zeros (RPZ's). Two new algorithms will be presented: one corrects a stripe stagnation problem from only a single reconstruction; the other modifies the IFTA to allow it to use locations of RPZ's as an additional constraint and prevents stripe stagnation from occurring altogether.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"78 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":"131473011","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":"Signal Processing in Higher Dimensions","authors":"A. Lohmann","doi":"10.1364/srs.1989.wa1","DOIUrl":"https://doi.org/10.1364/srs.1989.wa1","url":null,"abstract":"Suppose the signal is u(t). Two examples of representations in artifical and/or higher dimensions are the autocorrelation: and the (auto-)triple correlation: Isn't it masochistic to deal with these indirect representations of the signal instead of with the signal u(t) itself? The triple correlation is an example of artificial increase of dimensionality. The signal u(t) is ID, the triple correlation u3(t1,t2) is 2D.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"23 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":"129463862","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":"Feasible Cone Beam Scanning Methods for Exact 3-D Tomographic Image Reconstruction","authors":"H. Kudo, Tsuneo Saito","doi":"10.1364/srs.1989.fd3","DOIUrl":"https://doi.org/10.1364/srs.1989.fd3","url":null,"abstract":"Considerable efforts have been made for visualizing 3-D structures of human organs by x-ray tomography. From the view point of the data collection time, the cone beam method with a circular source motion is promising for this purpose. However, the exact 3-D image reconstruction from the cone beam projections is a troublesome and time-consuming problem, because the solution cannot be decomposed into 2-D transaxial slices. For this difficulty, approximate reconstruction algorithms are proposed and practically used in many application areas [1,2]. Unfortunately, these algorithms suffer from the degradation of reconstructed images when the cone angle is large.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"10 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113956895","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":"Necessary and sufficient conditions for the existence and synthesis of bipolar incoherent pointspread functions","authors":"J. Mait","doi":"10.1364/srs.1989.thc4","DOIUrl":"https://doi.org/10.1364/srs.1989.thc4","url":null,"abstract":"In 1978 Lohmann and Rhodes [1] presented a general two-channel hybrid system for bipolar incoherent spatial filtering. The work by Lohmann and Rhodes is significant in that it presented a unified and compact analysis of such filtering. Subsequent work by Mait [2,3] is also significant for its consideration of synthesis, or design, of such systems so as to produce a specific bipolar response.","PeriodicalId":193110,"journal":{"name":"Signal Recovery and Synthesis III","volume":"129 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":"126901711","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}