Three methods for reconstructing objects from x rays: A comparative study

Herman, Labor T.; Rowland, Stuart W.

doi:10.1016/0146-664x(73)90025-7

Cited by 68 publications

(7 citation statements)

References 6 publications

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“…The whole problem can be described as minimization of the differences between original (measured) and calculated projections:Various algebraic techniques use different criteria to estimate these errors and to apply corrections. They can be subdivided into four groups: ART, algebraic reconstruction technique;(176) SIRT,(177) simultaneous iterative reconstruction technique; SART, simultaneous algebraic reconstruction technique;(177) and RMLE, relaxation methods for linear equations. 170,178,179 …”

Section: D Reconstructionmentioning

confidence: 99%

Structural Analysis of Macromolecular Assemblies by Electron Microscopy

2011

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Introduction 7711 1.1. Light and Electron Microscopy and Their Impact in Biology 7711 1.2. EM of Macromolecular Assemblies, Isolated and in Situ 7711 2. EM Imaging 7711 2.1. Sample Preparation 7711 2.1.1. Negative Staining of Isolated Assemblies 7712 2.1.2. Cryo EM of Isolated and Subcellular Assemblies 7712 2.1.3. Stabilization of Dynamic Assemblies 7713 2.1.4. EM Preparation of Cells and Tissues 7713 2.2. Interaction of Electrons with the Specimen 7714 2.

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Section: D Reconstructionmentioning

confidence: 99%

Structural Analysis of Macromolecular Assemblies by Electron Microscopy

2011

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“…Theorem 4, especially in conjunction with Theorem 2, indicates that versions of Algorithm 2 may nevertheless yield reasonable results (this has been found so in practice [2,4,7,8,10]); however, the limiting behavior of the algorithm is no longer guaranteed, and has, in fact, been found quite bad (see, e.g., [7]). …”

Section: Practical Considerationsmentioning

confidence: 87%

“…Some of the other papers mentioning similar methods for image reconstruction are [2,5,6,7,8,10]. Such algorithms are commonly referred to as 17'0 ART (algebraic reconstruction techniques).…”

Section: The Relaxation Methods and Its Convergencementioning

confidence: 99%

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Iterative relaxation methods for image reconstruction

Herman¹,

Lent

Lutz³

1975

Proceedings of the 1975 Annual Conference on - ACM 75

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The problem of recovering an image (a function of two variables) from experimentally available integrals of its grayness over thin strips is of great importance in a large number of scientific areas.An important version of the problem in medicine is that of obtaining the exact density distribution within the human body from X-ray projections.One approach that has been taken to solve this problem consists of translating the available information into a system of linear inequalities.The size and the sparsity of the resulting system of inequalities (typically, 25,000 inequalities with less than 1% of the coefficients nonzero) makes methods using successive relaxations computationally attractive.A variety of such methods have been proposed with differing relaxation parameters.In this paper we show that for a consistent system of linear inequalities, any sequence of relaxation parameters lying strictly between zero and two generates a sequence of vectors which converges to a solution.Under the same assumptions, for a system of linear equations, the relaxation method converges to the minimum norm solution.Previously proposed techniques are shown to be special cases of our procedure with different choices of relaxation parameters.Thus, our results provide proofs of convergence for previously used algorithms where no such proofs existed before.We discuss the practical consequences for image reconstruction of the choice of the relaxation parameters.

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“…In fact, the "random variation" (usually called "noise") in x-ray transmission measurements may not be bandlimited theoretically. Subsequent investigators [23,65,117] have suggested various bandlimiting windows that reduce the propagation and amplification of noise by the reconstruction. These issues have been investigated by simulation, and investigators continue to pursue these issues by using either a computer phantom [57] described by Shepp and Logan [117] or different ones like Defrise and CD-phantom (for cone-beam system).…”

Section: C-object Reconstructionmentioning

confidence: 99%

How Random is Your Tomographic Noise? A Number Theoretic Transform (NTT) Approach

Fiorini

2014

Fundamenta Informaticae

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Discrete Tomography (DT), differently from GT and CT, focuses on the case where only few specimen projections are known and the images contain a small number of different colours (e.g. black-and-white). A concise review on main contemporary physical and mathematical CT system problems is offered. Stochastic vs. Combinatorially Optimized Noise generation is compared and presented by two visual examples to emphasise a major double-bind problem at the core of contemporary most advanced instrumentation systems. Automatic tailoring denoising procedures to real dynamic system characteristics and performance can get closer to ideal self-registering and selflinearizing system to generate virtual uniform and robust probing field during its whole designed service life-cycle. The first attempt to develop basic principles for system background low-level noise source automatic characterization, profiling and identification by CICT, from discrete system parameter, is presented. As a matter of fact, CICT can supply us with cyclic numeric sequences perfectly tuned to their low-level multiplicative source generators, related to experimental high-level overall perturbation (according to high-level classic perturbation computational model under either additive or multiplicative perturbation hypothesis). Numeric examples are presented. Furthermore, a practical NTT example is given. Specifically, advanced CT system, HRO and Mission Critical Project (MCP) for very low Technological Risk (TR) and Crisis Management (CM) system will be highly benefitted mostly by CICT infocentric worldview. The presented framework, concepts and techniques can be used to boost the development of next generation algorithms and advanced applications quite conveniently.

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Three methods for reconstructing objects from x rays: A comparative study

Cited by 68 publications

References 6 publications

Structural Analysis of Macromolecular Assemblies by Electron Microscopy

Structural Analysis of Macromolecular Assemblies by Electron Microscopy

Iterative relaxation methods for image reconstruction

How Random is Your Tomographic Noise? A Number Theoretic Transform (NTT) Approach

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