Related papers: The Radon cumulative distribution transform and it…
This paper introduces the `Projectron' as a new neural network architecture that uses Radon projections to both classify and represent medical images. The motivation is to build shallow networks which are more interpretable in the medical…
This paper describes an effective and efficient image classification framework nominated distributed deep representation learning model (DDRL). The aim is to strike the balance between the computational intensive deep learning approaches…
We find a new and simple inversion formula of the Radon transform RT with the only use of the shearlet system and of well-known properties of RT. No intertwining relation of differential operators in Euclidean space and Radon domain is…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
Recent progress in image recognition has stimulated the deployment of vision systems at an unprecedented scale. As a result, visual data are now often consumed not only by humans but also by machines. Existing image processing methods only…
Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of kinetic equations. Relation of probability density on phase space for…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…
Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as…
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…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
Tabular data have been extensively used in different knowledge domains. Convolutional neural networks (CNNs) have been successfully used in many applications where important information about data is embedded in the order of features…
In this work we consider the Conical Radon Transform, which integrates a function on $\R^n$ over families of circular cones. Transforms of this type are known to arise naturally as models of Compton camera imaging and single-scattering…
Existing unpaired low-light image enhancement approaches prefer to employ the two-way GAN framework, in which two CNN generators are deployed for enhancement and degradation separately. However, such data-driven models ignore the inherent…
The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…
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…
Tools from topological data analysis have been widely used to represent binary images in many scientific applications. Methods that aim to represent grayscale images (i.e., where pixel intensities instead take on continuous values) have…
Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear…
A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These…
This paper considers a convolutional neural network transformation that reduces computation complexity and thus speedups neural network processing. Usage of convolutional neural networks (CNN) is the standard approach to image recognition…