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Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints最新文献

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Image Reconstruction and Partial Deconvolution with Support Constraint Separation Angle and Least-Squares Interpolation Procedures 图像重建和部分反卷积支持约束分离角和最小二乘插值程序
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.fa13
A. Lannes
{"title":"Image Reconstruction and Partial Deconvolution with Support Constraint Separation Angle and Least-Squares Interpolation Procedures","authors":"A. Lannes","doi":"10.1364/srs.1983.fa13","DOIUrl":"https://doi.org/10.1364/srs.1983.fa13","url":null,"abstract":"In image reconstruction from projections [1], and more generally, in any partial deconvolution with support constraint, the central problem is to specify the conditions under which it is possible to interpolate, in a bounded region W, the Fourier transform of an object function with support in a bounded region V [2,3,4]. In particular, it is then essential to understand, in an analytical way, the parts played by the size of V and W, and the geometry of the whole V, W-configuration (cf. for example Fig. 1). The aim of this communication is to summarize the corresponding analysis, and to visualize the main results with the aid of appropriate representations.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","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":"117005520","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}
引用次数: 1
Spectrum extrapolation on a finite band 有限频带上的频谱外推
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.wa16
F. Gori, S. Wabnitz
{"title":"Spectrum extrapolation on a finite band","authors":"F. Gori, S. Wabnitz","doi":"10.1364/srs.1983.wa16","DOIUrl":"https://doi.org/10.1364/srs.1983.wa16","url":null,"abstract":"The iterative method of Gerchberg (GM) for extrapolating the whole spectrum of a finite support object1 has been analyzed and generalized by several authors2-14. In principle, during each iteration of the GM an infinite band of frequencies should be handled. At first sight, it seems that the (obvious) existence of a cut-off frequency in any practical implementation of the GM should simply allow the spectrum extrapolation to be achieved only below such a frequency. This is not the case, as we shall presently show, in that the extrapolated spectrum obtained by this method up to the cut-off frequency does not coincide with the true spectrum. In this paper we present a modified version of the GM that allows to obtain a spectrum extrapolation on a finite band of frequencies. This is of use both to limit the storage and computation time requirements and to reduce the sensitivity to high frequency noise.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","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":"132471652","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}
引用次数: 0
Singular Value Analyses of Inversion of Laplace and Optical Imaging Transforms 拉普拉斯反演与光学成像变换的奇异值分析
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.tha20
M. Bertero, E. Pike
{"title":"Singular Value Analyses of Inversion of Laplace and Optical Imaging Transforms","authors":"M. Bertero, E. Pike","doi":"10.1364/srs.1983.tha20","DOIUrl":"https://doi.org/10.1364/srs.1983.tha20","url":null,"abstract":"The use of the eigenvalues and eigenfunctions of the first order Fredholm equations describing optical imaging has long been known. The eigenvalues and eigenfunctions of the first order Fredholm equation of the Laplace transform have only recently been discovered and similarly used (McWhirter and Pike 1978). Let us consider for simplicity the one dimensional case with magnification unity. For an eigenfunction to be defined the linear mapping A:f → g of the \"object\" f into its \"image\" g must define a compact bijective operator A of, say, L2 (−1,+1) into itself.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","volume":"32 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":"115354810","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}
引用次数: 0
The Phase Problem of X-Ray Crystallography from the Viewpoint of Signal Recovery 从信号恢复的角度看x射线晶体学的相位问题
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.fa12
G. Bricogne
{"title":"The Phase Problem of X-Ray Crystallography from the Viewpoint of Signal Recovery","authors":"G. Bricogne","doi":"10.1364/srs.1983.fa12","DOIUrl":"https://doi.org/10.1364/srs.1983.fa12","url":null,"abstract":"The diffraction of X-rays by crystals was discovered in 1912 by Laue who proposed a theory of the phenomenon based on its analogy with optical diffraction by gratings. It is most easily understood from the standpoint of Fourier analysis, in which language it was reformulated shortly afterwards. The electron density in a crystal is periodic, and may therefore be conceived as a superposition of plane waves whose wave vectors belong to a \"reciprocal lattice\" dual to the crystal lattice. The contribution of each wave, or system of fringes, is described by a complex Fourier coefficient, whose amplitude gives the strength of this system of fringes, and whose phase determines the position of the fringes relative to some fixed origin. If all the amplitudes and phases of these waves are known, it is possible to obtain a picture of the electron distribution in the crystal by superposing them; that is, by a simple Fourier synthesis.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","volume":"47 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":"115019066","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}
引用次数: 0
Dependent and Independent Constraints for a Multiple Objective Iterative Algorithm 多目标迭代算法的独立约束与相关约束
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.tha14
J. Mait, W. Rhodes
{"title":"Dependent and Independent Constraints for a Multiple Objective Iterative Algorithm","authors":"J. Mait, W. Rhodes","doi":"10.1364/srs.1983.tha14","DOIUrl":"https://doi.org/10.1364/srs.1983.tha14","url":null,"abstract":"Constrained iterative algorithms have been applied primarily to single objective applications,1 where by objective we mean that distribution that is to be reconstructed from partial information or synthesized with desired characteristics. In a recent work by the authors,2 Fienup's error-reduction algorithm was extended to multiple objectives, as shown in Fig. 1, and was applied to a specific synthesis problem with two objectives. In this paper, we illustrate an important characteristic of multiple objective iterative algorithms, dependent constraints.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","volume":"12 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":"116946817","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}
引用次数: 0
Incorporation of Prior Constraints in Tomographic Reconstructions from Coded Images 基于先验约束的编码图像层析重建
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.fa8
R. Paxman, G. Gindi, H. Barrett
{"title":"Incorporation of Prior Constraints in Tomographic Reconstructions from Coded Images","authors":"R. Paxman, G. Gindi, H. Barrett","doi":"10.1364/srs.1983.fa8","DOIUrl":"https://doi.org/10.1364/srs.1983.fa8","url":null,"abstract":"The study of coded-aperture imaging has usually centered on the restoration of planar objects from planar coded images. The concept has been generalized to the problem of restoring a 3-dimensional object from a planar coded image. These two tasks are illustrated in Figure 1.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","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":"130745398","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}
引用次数: 0
Phase Retrieval from Intensity Data degraded by Shot-Noise 从弹噪声退化的强度数据中提取相位
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.tha2
C. Slump, H. Ferwerda
{"title":"Phase Retrieval from Intensity Data degraded by Shot-Noise","authors":"C. Slump, H. Ferwerda","doi":"10.1364/srs.1983.tha2","DOIUrl":"https://doi.org/10.1364/srs.1983.tha2","url":null,"abstract":"In the paper by one of us (H.A.F.) [1], the phase problem was reviewed for circumstances under which the stochastic character of the image could be ignored. A statistical description becomes imperative for images obtained under low-intensity illumination as occurs e.g. in low-dose electron microscopy. Under these circumstances the images are heavily degraded by shot-noise. Often(e.g. [2,3])images are described as a signal plus signal-independent noise. Such a treatment does not apply to shot-noise, the quanta arriving in non-overlapping image cells are statistically independent Poisson-distributed random variables [4]. The variances of the data-counts also contain information about the signal. In this contribution we discuss the retrieval of the object wave function (w.f.) from shot-noise degraded images. Due to the stochastic imaging process, the reconstructed object w.f. is also stochastic. The purpose of this contribution is to establish the statistical characterization of the object w.f. We assume axial coherent quasi-monochromatic illumination. The analysis is presented for one lateral dimension only, the extension to two dimensions is obvious.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","volume":"16 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":"124013864","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}
引用次数: 0
LBI Image Recovery Using Sharpness Maximization 使用锐度最大化的LBI图像恢复
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.fa14
D. Steer, M. Ito, P. Dewdney
{"title":"LBI Image Recovery Using Sharpness Maximization","authors":"D. Steer, M. Ito, P. Dewdney","doi":"10.1364/srs.1983.fa14","DOIUrl":"https://doi.org/10.1364/srs.1983.fa14","url":null,"abstract":"In radio Long Baseline Interferometry (LBI), the image is recovered from measurements made in the aperture plane. However, two major difficulties hinder the imaging process.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","volume":"24 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":"125238571","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}
引用次数: 0
An Algorithm for Incomplete Range of Views Reconstruction 一种不完全视野重构算法
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.fa1
H. Tuy
{"title":"An Algorithm for Incomplete Range of Views Reconstruction","authors":"H. Tuy","doi":"10.1364/srs.1983.fa1","DOIUrl":"https://doi.org/10.1364/srs.1983.fa1","url":null,"abstract":"To reconstruct a cross-section of a 3D object, most algorithms require knowledge of the projection data in a full range of views [1]. In some practical situations [2, 3], reconstruction from an incomplete range of views is inevitable although it is not desirable from a mathematical point of view. Objects to be reconstructed are of compact support. Their Fourier transforms can be extended to an entire function of exponential growth (band-limited function). Consequently, there is a unique solution to the incomplete range of views reconstruction problem. On the other hand, the problem is an ill-posed problem. For example, it has been indicated [4] that the spectrum of the singular values of the Radon transform for limited range of views is split up into_two parts. One part consists of singular values near one, and the other part consists of singular values near zero. The recovery of small singular values is necessary for a process to reconstruct objects with good quality. This, however, exacerbates instability in the process, i.e., a small error in the projection data might lead to an undesirable large difference in reconstructed images. Making use of a priori information on image and projection data is being examined to reduce this instability.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","volume":"16 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":"122066601","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}
引用次数: 2
Image Registration; The Undersampled Case 图像配准;样本不足的情况
Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints Pub Date : 1900-01-01 DOI: 10.1364/srs.1983.tha18
P. Barry, M. Klop, J. D. Hulsmann
{"title":"Image Registration; The Undersampled Case","authors":"P. Barry, M. Klop, J. D. Hulsmann","doi":"10.1364/srs.1983.tha18","DOIUrl":"https://doi.org/10.1364/srs.1983.tha18","url":null,"abstract":"The registration of a multi-frame sequence of images has been a classic problem in image processing whose solution has found wide application in such diverse areas as astronomy, earth resource analysis, electron microscopy, computed-aided medical imaging, military surveillance and photo-reconnaissance. In the most general sense, precise image registration allows such subsequent processing as signal-to-noise improvement, pattern enhancement and characterization, and the automated detection of spatio-temporally varying patterns, to be carried out at a level that would be impossible if the image sequence were not accurately registered.","PeriodicalId":279385,"journal":{"name":"Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints","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":"126524491","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}
引用次数: 1
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