Search Results (3)

The convolution of two physical entities, denoted as f and g, delineates the manner in which one entity undergoes modification in response to the other. This transformative process is mathematically represented by the expression f ⨂ g, symbolizing the convolution of the two entities in a resultant function h. Frequently, it becomes imperative to comprehend the magnitude of the induced modifications. From the derived function h, a crucial step involves the separation of the two original signals, a process commonly referred to as deconvolution. Various techniques have been proposed to facilitate the calculation of the deconvolution, with one notable approach originating in 1931 by van Cittert. The algorithm, based on an iterative method, has been scrutinized over time, notably by Bracewell and, more recently, by Jansson. This work represents the current state-of-the-art, focusing specifically on the analysis of Auger spectra obtained through XPS. Emphasis is placed on delineating the procedural aspects of the analysis, and the algorithm utilized in the open-source software RxpsG is comprehensively described. Full article

The reconstruction of MRI data assumes a uniform radio-frequency field. However, in practice, the radio-frequency field is inhomogeneous and leads to anatomically inconsequential intensity non-uniformities across an image. An anatomic region can be imaged with multiple contrasts reconstructed independently and be suffering from different non-uniformities. These artifacts can complicate the further automated analysis of the images. A method is presented for the joint intensity uniformity restoration of two such images. The effect of the intensity distortion on the auto-co-occurrence statistics of each image as well as on the joint-co-occurrence statistics of the two images is modeled and used for their non-stationary restoration followed by their back-projection to the images. Several constraints that ensure a stable restoration are also imposed. Moreover, the method considers the inevitable differences between the signal regions of the two images. The method has been evaluated extensively with BrainWeb phantom brain data as well as with brain anatomic data from the Human Connectome Project (HCP) and with data of Parkinson’s disease patients. The performance of the proposed method has been compared with that of the N4ITK tool. The proposed method increases tissues contrast at least $4.62$ times more than the N4ITK tool for the BrainWeb images. The dynamic range with the N4ITK method for the same images is increased by up to +29.77%, whereas, for the proposed method, it has a corresponding limited decrease of $-1.15\%$ , as expected. The validation has demonstrated the accuracy and stability of the proposed method and hence its ability to reduce the requirements for additional calibration scans. Full article

In this report, we present several results in the theory of $\alpha$ -models of turbulence with improved accuracy that have been developed in recent years. The $\alpha$ -models considered herein are the Leray- $\alpha$ model, the zeroth Approximate Deconvolution Model (ADM) turbulence model, the modified Leray- $\alpha$ and the Navier–Stokes- $\alpha$ model. For all of the models from above, the accuracy is limited to ${\alpha }^2$ in smooth flow regions. Better accuracy requires decreasing the filter radius $\alpha$ , which, in turn, requires a smaller mesh width that will lead in the end to a higher computational cost. Instead, one can use approximate deconvolution (without decreasing the mesh size) to attain better accuracy. Such deconvolution methods have been considered recently in many studies that show the efficiency of this approach. For smooth flows, periodic boundary conditions and van Cittert deconvolution operator of order N, the expected accuracy is ${\alpha }^{2N+2}$ . In a bounded domain, such results are valid only in case special conditions are satisfied. In more general conditions, the author has recently proved that, in the case of the ADM, the expected accuracy of the finite element method with Taylor–Hood elements and Crank–Nicolson time stepping method is $\Delta t^2+h^2+K^N{\alpha }^2$ , where the constant $K<1$ depends on the ratio $\alpha /h$ , which is assumed constant. In this study, we present the extension of the result to the rest of the models. Full article