The derivation of the noise covariance of the ith projection view in Equation (5) is similar to the Appendix of Tilley et al. [22]; the difference is that our application is for DBT geometry in which the imaged volume is very close to the detector. As a result, we neglect the focal spot blur so the blurring operation in our study only includes the detector blur. For the directly measured projec...

The interpretation of these strings, as the characters used suggest, is that pal is a function that produces a palindrome from its argument and rpt is a function that produces a repeat of its first argument a number of times specified by its second argument. Note that although p, a, l, r, and t, are individual constant characters in the L-System, pal and rpt can be treated as strings during int...

Abstract Technology-enhanced Reciprocal Peer Tutoring (RPT) was carried out with Finnish, nine to ten year-old primary school students (N=40). The RPT as a method of paired mathematics placed specific emphasis on electrical mathematical writing and drawing. Little is known about the important area implementing digital skills at level. contribution this study address research gap in Technologica...

Digital breast tomosynthesis (DBT) is an emerging 3D x-ray imaging modality in which tomographic sections of the breast are generated from a limited range of tube angles. Because non-normal x-ray incidence causes the image of an object to be translated in sub-pixel increments with increasing projection angle, it is demonstrated in this work that DBT is capable of super-resolution (i.e., sub-pix...

This paper seeks to extend the Fourier space properties of the discrete Radon transform, R(t,m), proposed by Matus and Flusser in [1], to expanded discrete projections, R(k, θ), where the wrapping of rays is removed. This expanded mode yields projections more akin to the continuous space sinogram. It is similar to the Mojette transform defined in [2], but has a pre-determined set of discrete pr...

In Computed Tomography (CT), two-dimensional (2-D) slices or three-dimensional (3-D) volumes of an object are reconstructed from many projected line-integrals (usually x-ray transmission data) around the object. As the data collection capabilities and reconstruction algorithms for CT have become more sophisticated over the years, the demands on computer systems have become correspondingly great...

We give a simple method for constructing a projection from a surface of revolution M onto the plane perpendicular to the rotation axis, which preserves areas. Then we use this projection for constructing a multiresolution analysis and a continuous wavelet transform, starting from the existing planar constructions. Thus, the wavelets on M inherit all the properties of the corresponding planar wa...

We present a model-based parallel algorithm for origin and orientation refinement for 3D reconstruction in cryoTEM. The algorithm is based upon the Projection Theorem of the Fourier Transform. Rather than projecting the current 3D model and searching for the best match between an experimental view and the calculated projections, the algorithm computes the Discrete Fourier Transform (DFT) of eac...

In this project, we propose a new algorithm that recovers the rigid motion parameters and the underlying density function from a set of noisy measurements of three dimensional (3D) density functions. We measure the Radon transform of each 3D function which are randomly rotated and translated version of a target function that we try to recover. Radon transform is a set of parallel line integrals...