Volume 1, Issue 2

A projection operator onto a closed convex set in Hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms. Moreover, it minimizes distance and is nonexpansive, and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds. In this paper, we exploit the properties of these operators t...

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The image restoration theory discussed in a previous paper by Youla and Webb [1] is applied to a simulated image and the results compared with the well-known method known as the Gerchberg-Papoulis algorithm. The results show that the method of image restoration by projection onto convex sets, by providing a convenient technique for utilizing a priori information, performs significantly better than...

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Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknown emission density λ = λ(x, y, z) generates, and is to be reconstructed from, the number of counts n*(d) in each of D detector units d. Within the model, we give an algorithm for determining an estimate λ of λ which maximizes the probability p(n*|λ) of observing the actual detector count data n* over all possible densities λ. Let independent Poisson variables n(b) with unknown means λ(b), b = 1, ···, B represent the number of unobserved emissions in each of B boxes (pixels) partitioning an object containing an emitter. Suppose each emission in box b is detected in detector unit d with probability p(b, d), d = 1, ···, D with p(b, d) a one-step transition matrix, assumed known. We observe the total number n* = n*(d) of emissions in each detector unit d and want to estimate the unknown λ = λ(b), b = 1, ···, B. For each λ, the observed data n* has probability or likelihood p(n*|λ). The EM algorithm of mathematical statistics starts with an initial estimate λ0 and gives the following simple iterative procedure for obtaining a new estimate λnew, from an old estimate λold, to obtain Σk, k = 1, 2, ···, λnew(b)= λold(b) λDd=1 n*(d)p(b,d)/Σλold(bΣ)p(bλ,d),b=1,···B.

先前的发射断层扫描（ET）模型未能区分ET与透射断层扫描的物理原理。我们提出了一个更精确的ET通用数学模型，其中未知的发射密度λ = λ(x, y, z)产生待重建的图像，并从每个探测器单元d的计数n*(d)中重建。在该模型内，我们给出了一种确定λ估计的算法...

A dye-edge tracking algorithm was used to determine the corresponding points in the two images (anterior-posterior and lateral) of the digital subtraction biplane angiography. This correspondence was used to reconstruct three-dimensional images of cerebral arteries in a dog experiment and a clinical observation. The method was tested by comparing the measured image of oblique view to the computed ...

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