We present a new method for rigid registration of CT scans in Radon space. The inputs are the two 3D Radon transforms of the CT scans, one densely sampled and the other sparsely sampled. The output s the rigid transformation that best matches them. The algorithm starts by finding the best matching between each direction vector in the sparse transform and the corresponding direction vector in th...

In this paper, we propose a rotation-invariant image watermarking scheme based on Radon transform. Rotation invariance is achieved using the translation property of the Radon transform. The radon transform emphasize and detect the linear characteristic to calculate the angle of image rotation. The image watermarking scheme used hologram quantization to spread the watermark information and analy...

The classical Radon transform can be thought of as a way to obtain the density of an n-dimensional object from its (n− 1)-dimensional sections in di erent directions. A generalization of this transform to in nite-dimensional spaces has the potential to allow one to obtain a function de ned on an in nite-dimensional space from its conditional expectations. We work within a standard framework in ...

Abstract This paper presents an investigation of the approximation property of neural networks with unbounded activation functions, such as the rectified linear unit (ReLU), which is the new de-facto standard of deep learning. The ReLU network can be analyzed by the ridgelet transform with respect to Lizorkin distributions. By showing three reconstruction formulas by using the Fourier slice the...

The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill-posed inverse problem that can be applied to X-ray tomography with polycrystalline materials. This paper is concerned with the development of a method to stably approximate the inverse of the noisy Radon transform on SO(3). The proposed approach is composed by basic building blocks of the coorbit theory o...

f(x) det(xx)dx and the Radon transform on the space Mn,m of n × m real matrices x = (xi,j). We present a self-contained proof of the Fourier transform formula for this distribution. Our method differs from that of J. Faraut and A. Korányi [FK] in the part related to justification of the corresponding Bernstein identity. We suggest a new proof of this identity based on explicit representation of...