The Teacher Education and Development Study in Mathematics, sponsored by the International Association for the Evaluation of Educational Achievement, is the first data-based study about mathematics teacher education with large-scale samples; this article is based on its data but develops a stand-alone conceptual framework to investigate the quality of teacher education among various countries. The framework includes five indicators: future teacher achievement, instructor effectiveness, coherence between universities and schools, courses/content arrangement, and overall effectiveness of teacher education programs. One of the findings provides indications that it is necessary to combine theoretical knowledge with practical teaching into teacher education; another finding is that for all countries involved, future teachers are less approving of the courses/content arrangement of teacher education programs than are program educators, thus perhaps lowering educators’ motivation to improve the arrangement. The data also indicate that there is a high degree of synchronization and organization in teacher education programs in the United States; however, these programs still require further development and promotion of their future teachers’ knowledge achievements.
Given that the computed tomography (CT) reconstruction algorithm based on compressed sensing (CS) results in blurred edges, we propose a modified Canny operator that assists the CS algorithm to accurately capture an object's edge, to preserve and further enhance the contrasts in the reconstructed image, thereby improving image quality. We modified two procedures of the traditional Canny operator, namely non-maximum suppression and edge tracking by hysteresis according to the characteristics of low-dose CT reconstruction, and proposed two major modifications: double-response edge detection and directional edge tracking. The newly modified Canny operator was combined with the CS reconstruction algorithm to become an edge-enhanced CS (EECS). Both a 2D Shepp-Logan phantom and a 3D dental phantom were used to conduct reconstruction testing. Root-mean-square error, peak signal-to-noise ratio, and universal quality index were employed to verify the reconstruction results. Qualitative and quantitative results of EECS reconstruction showed its superiority over conventional CS or CS combined with different edge detection techniques, such as Laplacian, Prewitt, Sobel operators, etc. The experiments verified that the proposed modified Canny operator is able to effectively detect the edge location of an object during low-dose reconstruction, enabling EECS to reconstruct images with better quality than those produced by other algorithms.
Digital periapical radiography is widely used in clinical dentistry because the technique is relatively simple and inexpensive. However, the main drawback of periapical radiography is that it represents a three-dimensional object in a two-dimensional film due to its inherent projection technique. The objective of this study was to develop a prototype intraoral computed tomosynthesis system, which can provide quasi-three-dimensional (so-called 2.5D) images. We developed a prototype intraoral computed tomosynthesis machine. Regular digital periapical radiography, computed tomosynthesis scanning, and computed tomography scanning of a human central incisor were performed. Then, reconstruction images obtained using computed tomosynthesis and computed tomography approaches were quantitatively evaluated using the signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR). From the experimental results, compared with periapical radiographic images, reconstruction images obtained using the computed tomosynthesis approach revealed detailed microstructures in different depth sections. In addition, the SNR and CNR of reconstruction images obtained using the computed tomography approach was better than those of the images obtained using the computed tomosynthesis approach. However, the differences could not be clearly identified by the naked eye. The preliminary experimental results indicate that an intraoral computed tomosynthesis system may be useful for clinical dental diagnosis.
To further reduce the noise and artifacts in the reconstructed image of sparse-view CT, we have modified the traditional total variation (TV) methods, which only calculate the gradient variations in x and y directions, and have proposed 8- and 26-directional (the multi-directional) gradient operators for TV calculation to improve the quality of reconstructed images. Different from traditional TV methods, the proposed 8- and 26-directional gradient operators additionally consider the diagonal directions in TV calculation. The proposed method preserves more information from original tomographic data in the step of gradient transform to obtain better reconstruction image qualities. Our algorithms were tested using two-dimensional Shepp–Logan phantom and three-dimensional clinical CT images. Results were evaluated using the root-mean-square error (RMSE), peak signal-to-noise ratio (PSNR), and universal quality index (UQI). All the experiment results show that the sparse-view CT images reconstructed using the proposed 8- and 26-directional gradient operators are superior to those reconstructed by traditional TV methods. Qualitative and quantitative analyses indicate that the more number of directions that the gradient operator has, the better images can be reconstructed. The 8- and 26-directional gradient operators we proposed have better capability to reduce noise and artifacts than traditional TV methods, and they are applicable to be applied to and combined with existing CT reconstruction algorithms derived from CS theory to produce better image quality in sparse-view reconstruction.
Limited-angle iterative reconstruction (LAIR) reduces the radiation dose required for computed tomography (CT) imaging by decreasing the range of the projection angle. We developed an image-quality-based stopping-criteria method with a flexible and innovative instrument design that, when combined with LAIR, provides the image quality of a conventional CT system. This study describes the construction of different scan acquisition protocols for micro-CT system applications. Fully-sampled Feldkamp (FDK)-reconstructed images were used as references for comparison to assess the image quality produced by these tested protocols. The insufficient portions of a sinogram were inpainted by applying a context encoder (CE), a type of generative adversarial network, to the LAIR process. The context image was passed through an encoder to identify features that were connected to the decoder using a channel-wise fully-connected layer. Our results evidence the excellent performance of this novel approach. Even when we reduce the radiation dose by 1/4, the iterative-based LAIR improved the full-width half-maximum, contrast-to-noise and signal-to-noise ratios by 20% to 40% compared to a fully-sampled FDK-based reconstruction. Our data support that this CE-based sinogram completion method enhances the efficacy and efficiency of LAIR and that would allow feasibility of limited angle reconstruction.
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