|
Osem (mathematics)
In mathematical optimization, the ordered subset expectation maximization (OSEM) method is an iterative method that is used in computed tomography. In applications in medical imaging, the OSEM method is used for positron emission tomography (PET), for single-photon emission computed tomography (SPECT), and for X-ray computed tomography An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ... (X-ray CT) scans. The OSEM method is related to the expectation–maximization (EM) method of statistics. The OSEM method is also related to methods of filtered back projection. References * Hudson, H.M., Larkin, R.S. (1994) "Accelerated image reconstruction using ordered subsets of projection data", ''IEEE Trans. Medical Imaging'', 13 (4), 601–609 Optimization algorithms and methods Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Method
In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''i''-th approximation (called an "iterate") is derived from the previous ones. A specific implementation with Algorithm#Termination, termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or Quasi-Newton method, quasi-Newton methods like Broyden–Fletcher–Goldfarb–Shanno algorithm, BFGS, is an algorithm of an iterative method or a method of successive approximation. An iterative method is called ''Convergent series, convergent'' if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In contrast, direct methods attempt to solve the problem by a finit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computed Tomography
A computed tomography scan (CT scan), formerly called computed axial tomography scan (CAT scan), is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers or radiology technologists. CT scanners use a rotating X-ray tube and a row of detectors placed in a gantry to measure X-ray attenuations by different tissues inside the body. The multiple X-ray measurements taken from different angles are then processed on a computer using tomographic reconstruction algorithms to produce tomographic (cross-sectional) images (virtual "slices") of a body. CT scans can be used in patients with metallic implants or pacemakers, for whom magnetic resonance imaging (MRI) is contraindicated. Since its development in the 1970s, CT scanning has proven to be a versatile imaging technique. While CT is most prominently used in medical diagnosis, it can also be used to form images of non-living objects. The 1979 N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medical Imaging
Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to reveal internal structures hidden by the skin and bones, as well as to diagnose and treat disease. Medical imaging also establishes a database of normal anatomy and physiology to make it possible to identify abnormalities. Although imaging of removed organ (anatomy), organs and Tissue (biology), tissues can be performed for medical reasons, such procedures are usually considered part of pathology instead of medical imaging. Measurement and recording techniques that are not primarily designed to produce images, such as electroencephalography (EEG), magnetoencephalography (MEG), electrocardiography (ECG), and others, represent other technologies that produce data susceptible to representation as a parameter graph versus time or maps that contain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positron Emission Tomography
Positron emission tomography (PET) is a functional imaging technique that uses radioactive substances known as radiotracers to visualize and measure changes in metabolic processes, and in other physiological activities including blood flow, regional chemical composition, and absorption. Different tracers are used for various imaging purposes, depending on the target process within the body, such as: * Fluorodeoxyglucose ( 18F">sup>18FDG or FDG) is commonly used to detect cancer; * 18Fodium fluoride">sup>18Fodium fluoride (Na18F) is widely used for detecting bone formation; * Oxygen-15 (15O) is sometimes used to measure blood flow. PET is a common imaging technique, a medical scintillography technique used in nuclear medicine. A radiopharmaceutical—a radioisotope attached to a drug—is injected into the body as a tracer. When the radiopharmaceutical undergoes beta plus decay, a positron is emitted, and when the positron interacts with an ordinary electron, the tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-photon Emission Computed Tomography
Single-photon emission computed tomography (SPECT, or less commonly, SPET) is a nuclear medicine tomography, tomographic imaging technique using gamma rays. It is very similar to conventional nuclear medicine planar imaging using a gamma camera (that is, scintigraphy), but is able to provide true 3D computer graphics, 3D information. This information is typically presented as cross-sectional slices through the patient, but can be freely reformatted or manipulated as required. The technique needs delivery of a gamma-emitting radioisotope (a radionuclide) into the patient, normally through injection into the bloodstream. On occasion, the radioisotope is a simple soluble dissolved ion, such as an Isotopes of gallium, isotope of gallium(III). Usually, however, a marker radioisotope is attached to a specific ligand to create a radioligand, whose properties bind it to certain types of tissues. This marriage allows the combination of ligand and radiopharmaceutical to be carried and bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expectation–maximization Algorithm
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the ''E'' step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step. It can be used, for example, to estimate a mixture of gaussians, or to solve the multiple linear regression problem. History The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin. They pointed out that the method had been "proposed man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization Algorithms And Methods
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Optimization problems can be divided into two categ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medical Statistics
Medical statistics (also health statistics) deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research. Medical statistics has been a recognized branch of statistics in the United Kingdom for more than 40 years, but the term has not come into general use in North America, where the wider term 'biostatistics' is more commonly used.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. However, "biostatistics" more commonly connotes all applications of statistics to biology. Medical statistics is a subdiscipline of statistics. It is the science of summarizing, collecting, presenting and interpreting data in medical practice, and using them to estimate the magnitude of associations and test hypotheses. It has a central role in medical investigations. It not only provides a way of organizing information on a wider and more formal basis than relying on the exchange of anecdot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
