Generative Noise Reduction in Dental Cone-Beam CT by a Selective Anatomy Analytic Iteration Reconstruction Algorithm

Dental cone-beam computed tomography (CBCT) is a powerful tool in clinical treatment planning, especially in a digital dentistry platform. Currently, the “as low as diagnostically acceptable” (ALADA) principle and diagnostic ability are a trade-off in most of the 3D integrated applications, especially in the low radio-opaque densified tissue structure. The CBCT benefits in comprehensive diagnosis and its treatment prognosis for post-operation predictability are clinically known in modern dentistry. In this paper, we propose a new algorithm called the selective anatomy analytic iteration reconstruction (SA2IR) algorithm for the sparse-projection set. The algorithm was simulated on a phantom structure analogous to a patient’s head for geometric similarity. The proposed algorithm is projection-based. Interpolated set enrichment and trio-subset enhancement were used to reduce the generative noise and maintain the scan’s clinical diagnostic ability. The results show that proposed method was highly applicable in medico-dental imaging diagnostics fusion for the computer-aided treatment planning, because it had significant generative noise reduction and lowered computational cost when compared to the other common contemporary algorithms for sparse projection, which generate a low-dosed CBCT reconstruction.

Fractal Structures of General Mandelbrot Sets and Julia Sets Generated from Complex Non-Analytic Iteration Fm(z)=z¯m+c

In this paper we use the same idea as the complex analytic dynamics to study general Mandelbrot sets and Julia sets generated from the complex non-analytic iteration . The definition of the general critical point is given, which is of vital importance to the complex non-analytic dynamics. The general Mandelbrot set is proved to be bounded, axial symmetry by real axis, and have (m+1)-fold rotational symmetry. The stability condition of periodic orbits and the boundary curve of stability region of one-cycle are given. And the general Mandelbrot sets are constructed by the escape-time method and the periodic scanning algorithm, which present a better understanding of the structure of the Mandelbrot sets. The filled-in Julia sets Km,c have m-fold structures. Similar to the complex analytic dynamics, the general Mandelbrot sets are kinds of mathematical dictionary or atlas that map out the behavior of the filled-in Julia sets for different values of c.

An Analytic Iteration Method of Geometrical Nonlinear Analysis for Frame Structures and its Application Program Research

Static method and energy method are two mainly solution methods for structure calculation presently. Static method often appears insoluble complicated transcendental equations and continues hardly. Energy method can solve force analysis of complicated structure and it is a widely used method at present, but in general it is not exact. In this article, analytic iterative method is a calculation method of analyzing geometrical nonlinear of frame Structures, considering the influence of geometrical nonlinear in structure calculation, on foundation of the analytic method that expressed with deflection equation of pressure column with geometry parameter expression with the combination of traditional linear analysis method. And a calculating application program is written to calculate displacement and force of frame structure in the environment of MATLAB language in order to apply conveniently. Because this method is on basis of analytic method, its results have sufficient accuracy. At last, there is an example to explain.

On Covariant Embeddings of a Linear Functional Equation with Respect to an Analytic Iteration Group

Let a(x), b(x), p(x) be formal power series in the indeterminate x over [Formula: see text] (i.e. elements of the ring [Formula: see text] of such series) such that ord a(x) = 0, ord p(x) = 1 and p(x) is embeddable into an analytic iteration group [Formula: see text] in [Formula: see text]. By a covariant embedding of the linear functional equation [Formula: see text] (for the unknown series [Formula: see text]) with respect to [Formula: see text]. In this paper we solve the system ((Co1), (Co2)) (of so-called cocycle equations) completely, describe when and how the boundary conditions (B1) and (B2) can be satisfied, and present a large class of equations (L) together with iteration groups [Formula: see text] for which there exist covariant embeddings of (L) with respect to [Formula: see text].

Some Differential Equations Related to Iteration Theory

In connection with the translation equation(T)three differential equations arise together with a differential initial condition. They are satisfied by the differentiable solutions of (T) and of the initial condition(I)These equations are attributed in [9] to E. Jabotinsky who seems to have been the first who treated these equations in connection with the theory of analytic iteration (see [6], cf. [7, 8], but see also [1, 2, 3]).Gronau (see [9]) asked whether, conversely, it is true that all solutions of each of these “Jabotinsky differential equations”, possibly with some further initial conditions added, are also solutions of the translation equation. In this paper we give counter examples but also partial positive answers to these questions. First we show how one obtains the Jabotinsky equations from (T) and (I).