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Iterative reconstruction refers to iterative algorithms used to reconstruct 2D and 3D images in certain imaging techniques. For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are a better, but computationally more expensive, alternative to the common filtered back projection (FBP) method, which directly calculates the image in a single reconstruction step.〔Herman, G. T., Fundamentals of computerized tomography: Image reconstruction from projection, 2nd edition, Springer, 2009〕 == Basic concepts == The reconstruction of an image from the acquired data is an inverse problem. Often, it is not possible to exactly solve the inverse problem directly. In this case, a direct algorithm has to approximate the solution, which might cause visible reconstruction artifacts in the image. Iterative algorithms approach the correct solution using multiple iteration steps, which allows to obtain a better reconstruction at the cost of a higher computation time. In computed tomography, this approach was the one first used by Hounsfield. There are a large variety of algorithms, but each starts with an assumed image, computes projections from the image, compares the original projection data and updates the image based upon the difference between the calculated and the actual projections. There are typically five components to iterative image reconstruction algorithms, e.g. .〔 J A Fessler, "Penalized weighted least-squares image reconstruction for positron emission tomography," IEEE Trans. on Medical Imaging, 13(2):290-300, June 1994. 〕 # An object model that expresses the unknown continuous-space function that is to be reconstructed in terms of a finite series with unknown coefficients that must be estimated from the data. # A system model that relates the unknown object to the "ideal" measurements that would be recorded in the absence of measurement noise. Often this is a linear model of the form , where represents the noise. # A statistical model that describes how the noisy measurements vary around their ideal values. Often Gaussian noise or Poisson statistics are assumed. Because Poisson statistics are closer to reality, it is more widely used. # A cost function that is to be minimized to estimate the image coefficient vector. Often this cost function includes some form of regularization. Sometimes the regularization is based on Markov random fields. # An algorithm, usually iterative, for minimizing the cost function, including some initial estimate of the image and some stopping criterion for terminating the iterations. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Iterative reconstruction」の詳細全文を読む スポンサード リンク
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