Search Results (7)

Background/Objectives: In digital radiography imaging, dual-layer flat-panel detectors (DFDs), in which two flat-panel detector layers are stacked with a minimal distance between the layers and appropriate alignment, are commonly used in material decompositions as dual-energy applications with a single x-ray exposure. DFDs also enable more efficient use of incident photons, resulting in x-ray images with improved noise power spectrum (NPS) and detection quantum efficiency (DQE) performances as single-energy applications. Purpose: Although the development of DFD systems for material decomposition applications is actively underway, there is a lack of research on whether single-energy applications of DFD can achieve better performance than the single-layer case. In this paper, we experimentally observe the DFD performance in terms of the modulation transfer function (MTF), NPS, and DQE with discussions. Methods: Using prototypes of DFD, we experimentally measure the MTF, NPS, and DQE of the convex combination of the images acquired from the upper and lower detector layers of DFD. To optimize DFD performance, a two-step image registration is performed, where subpixel registration based on the maximum amplitude response to the transform based on the Fourier shift theorem and an affine transformation using cubic interpolation are adopted. The DFD performance is analyzed and discussed through extensive experiments for various scintillator thicknesses, x-ray beam conditions, and incident doses. Results: Under the RQA 9 beam conditions of 2.7 μGy dose, the DFD with the upper and lower scintillator thicknesses of 0.5 mm could achieve a zero-frequency DQE of 75%, compared to 56% when using a single-layer detector. This implies that the DFD using 75 % of the incident dose of a single-layer detector can provide the same signal-to-noise ratio as a single-layer detector. Conclusions: In single-energy radiography imaging, DFD can provide better NPS and DQE performances than the case of the single-layer detector, especially at relatively high x-ray energies, which enables low-dose imaging. Full article

Background: For a single exposure in radiography, a dual-layer flat-panel detector (DFD) can provide spectral images and efficiently utilize the transmitted X-ray photons to improve the detective quantum efficiency (DQE) performance. In this paper, to acquire high DQE performance, we present a registration method for X-ray images acquired from a DFD, considering only spatial translations and scale factors. The conventional registration methods have inconsistent estimate accuracies depending on the captured object scene, even when using entire pixels, and have deteriorated frequency performance because of the interpolation method employed. Methods: The proposed method consists of two steps; the first step is conducting a spatial translation according to the Fourier shift theorem with a subpixel registration, and the second step is conducting a scale transformation using cubic interpolation to process the X-ray projections. To estimate the subpixel spatial translation, a maximum-amplitude method using a small portion of the slant-edge phantom is used. Results: The performance of the proposed two-step method is first theoretically analyzed and then observed by conducting extensive experiments and measuring the noise power spectrum and DQE. An example for registering chest images is also shown. For a DFD, the proposed method shows a better registration result than the conventional one-step registration. The DQE improvement was more than 56% under RQA 9 compared to the single flat-panel detector case. Conclusions: The proposed two-step registration method can efficiently provide aligned image pairs from the DFD to improve the DQE performance at low doses and, thus, increase the accuracy of clinical diagnosis. Full article

We extend previous research to derive three additional M-1-dimensional integral representations over the interval $[0,1]$. The prior version covered the interval $[0,\infty ]$. This extension applies to products of M Slater orbitals, since they (and wave functions derived from them) appear in quantum transition amplitudes. It enables the magnitudes of coordinate vector differences (square roots of polynomials) $|{\mathbf{x}}_1-{\mathbf{x}}_2|=\sqrt{x_1^2-2x_1{x}_{2}cos\theta +x_2^2}$ to be shifted from disjoint products of functions into a single quadratic form, allowing for the completion of its square. The M-1-dimensional integral representations of M Slater orbitals that both this extension and the prior version introduce provide alternatives to Fourier transforms and are much more compact. The latter introduce a 3M-dimensional momentum integral for M products of Slater orbitals (in M separate denominators), followed in many cases by another set of M-1-dimensional integral representations to combine those denominators into one denominator having a single (momentum) quadratic form. The current and prior methods are also slightly more compact than Gaussian transforms that introduce an M-dimensional integral for products of M Slater orbitals while simultaneously moving them into a single (spatial) quadratic form in a common exponential. One may also use addition theorems for extracting the angular variables or even direct integration at times. Each method has its strengths and weaknesses. We found that these M-1-dimensional integral representations over the interval $[0,1]$ are numerically stable, as was the prior version, having integrals running over the interval $[0,\infty ]$, and one does not need to test for a sufficiently large upper integration limit as one does for the latter approach. For analytical reductions of integrals arising from any of the three, however, there is the possible drawback for large M of there being fewer tabled integrals over $[0,1]$ than over $[0,\infty ]$. In particular, the results of both prior and current representations have integration variables residing within square roots asarguments of Macdonald functions. In a number of cases, these can be converted to Meijer G-functions whose arguments have the form $(a{x}^2+bx+c)/x$, for which a single tabled integral exists for the integrals from running over the interval $[0,\infty ]$ of the prior paper, and from which other forms can be found using the techniques given therein. This is not so for integral representations over the interval $[0,1]$. Finally, we introduce a fourth integral representation that is not easily generalizable to large M but may well provide a bridge for finding the requisite integrals for such Meijer G-functions over $[0,1]$. Full article

In this study, the Wigner–Ville distribution is associated with the one sided Clifford–Fourier transform over ${\mathbb{R}}^n$, n = 3(mod 4). Accordingly, several fundamental properties of the WVD-CFT have been established, including non-linearity, the shift property, dilation, the vector differential, the vector derivative, and the powers of $\tau \in {\mathbb{R}}^n$. Moreover, powerful results on the WVD-CFT have been derived such as Parseval’s theorem, convolution theorem, Moyal’s formula, and reconstruction formula. Eventually, we deduce a directional uncertainty principle associated with WVD-CFT. These types of results, as well as methodologies for solving them, have applications in a wide range of fields where symmetry is crucial. Full article

This paper introduces definitions of the octonion cross Wigner distribution (OWD) and the octonion ambiguity function, forming a pair of octonion Fourier transforms. The main part is devoted to the study of the basic properties of the OWD. Among them are the properties concerning its nature (nonlinearity, parity, space support conservation, marginals) and some “geometric” transformations (space shift, space scaling) similar to the case of the complex Wigner distribution. This paper also presents specific forms of the modulation property and an extended discussion about the validity of Moyal’s formula and the uncertainty principle, accompanied by new theorems and examples. The paper is illustrated with examples of 3-D separable Gaussian and Gabor signals. The concept of the application of the OWD for the analysis of multidimensional analytic signals is also proposed. The theoretical results presented in the papers are summarized, and the possibility of further research is discussed. Full article

In this paper, the solvability of a class of convolution equations is discussed by using two-dimensional (2D) fractional Fourier transform (FRFT) in polar coordinates. Firstly, we generalize the 2D FRFT to the polar coordinates setting. The relationship between 2D FRFT and fractional Hankel transform (FRHT) is derived. Secondly, the spatial shift and multiplication theorems for 2D FRFT are proposed by using this relationship. Thirdly, in order to analyze the solvability of the convolution equations, a novel convolution operator for 2D FRFT is proposed, and the corresponding convolution theorem is investigated. Finally, based on the proposed theorems, the solvability of the convolution equations is studied. Full article

Geospatial co-registration is a mandatory prerequisite when dealing with remote sensing data. Inter- or intra-sensoral misregistration will negatively affect any subsequent image analysis, specifically when processing multi-sensoral or multi-temporal data. In recent decades, many algorithms have been developed to enable manual, semi- or fully automatic displacement correction. Especially in the context of big data processing and the development of automated processing chains that aim to be applicable to different remote sensing systems, there is a strong need for efficient, accurate and generally usable co-registration. Here, we present AROSICS (Automated and Robust Open-Source Image Co-Registration Software), a Python-based open-source software including an easy-to-use user interface for automatic detection and correction of sub-pixel misalignments between various remote sensing datasets. It is independent of spatial or spectral characteristics and robust against high degrees of cloud coverage and spectral and temporal land cover dynamics. The co-registration is based on phase correlation for sub-pixel shift estimation in the frequency domain utilizing the Fourier shift theorem in a moving-window manner. A dense grid of spatial shift vectors can be created and automatically filtered by combining various validation and quality estimation metrics. Additionally, the software supports the masking of, e.g., clouds and cloud shadows to exclude such areas from spatial shift detection. The software has been tested on more than 9000 satellite images acquired by different sensors. The results are evaluated exemplarily for two inter-sensoral and two intra-sensoral use cases and show registration results in the sub-pixel range with root mean square error fits around 0.3 pixels and better. Full article