Related papers: Three-dimensional multiscale discrete Radon and Jo…
We derive an explicit inversion algorithm for the spherical Radon transform in odd dimensions with partial radial data. We prove that the reconstruction of the unknown function can be reduced to solving ordinary differential equations,…
There exist two groups of electron microscopy methods that are capable of providing three-dimensional (3D) structural information of an object, i.e., electron tomography and depth sectioning. Electron tomography is capable of resolving…
This paper presents a two-step algorithm for online trajectory planning in indoor environments with unknown obstacles. In the first step, sampling-based path planning techniques such as the optimal Rapidly exploring Random Tree (RRT*)…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
An algorithm to efficiently compute the moments of volumetric images is disclosed. The approach demonstrates a reduction in processing time by reducing the computational complexity significantly. Specifically, the algorithm reduces…
Dense 3D convolutions provide high accuracy for perception but are too computationally expensive for real-time robotic systems. Existing tri-plane methods rely on 2D image features with interpolation, point-wise queries, and implicit MLPs,…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
We study the spherical slice transform which assigns to a function on the $n$-dimensional unit sphere the integrals of that function over cross-sections of the sphere by $k$-dimensional affine planes passing through the north pole. These…
This paper aims to solve a fundamental problem in intensity-based 2D/3D registration, which concerns the limited capture range and need for very good initialization of state-of-the-art image registration methods. We propose a regression…
Phantoms can serve as a gold standard for the validation of MRI numerical methods. In some special cases, it is possible to compute analytically the Radon transform, or sinogram, of a phantom. In this work, we present analytical formulae to…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…
I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT) described algorithmically by a combination of chirp transforms and ordinary DFTs. The transform is shown to be consistent with a continuous two-dimensional rotation…
Planning safe paths in 3D workspace for high DoF robotic systems, such as manipulators, is a challenging problem, especially when the environment is populated with the dynamic obstacles that need to be avoided. In this case the time…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
Due to its remarkable energy compaction properties, the discrete cosine transform (DCT) is employed in a multitude of compression standards, such as JPEG and H.265/HEVC. Several low-complexity integer approximations for the DCT have been…
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
The 3D Discrete Fourier Transform (DFT) is a technique used to solve problems in disparate fields. Nowadays, the commonly adopted implementation of the 3D-DFT is derived from the Fast Fourier Transform (FFT) algorithm. However, evidence…
This project is aimed at designing the fast forward projection algorithm and also the backprojection algorithm for cone beam CT imaging systems with circular X-ray source trajectory. The principle of the designs is based on utilizing the…