Related papers: Radon-Nikodym approximation in application to imag…
Radon--Nikodym approach to relaxation dynamics, where probability density is built first and then used to calculate observable dynamic characteristic is developed and applied to relaxation type signals study. In contrast with $L^2$ norm…
For distribution regression problem, where a bag of $x$--observations is mapped to a single $y$ value, a one--step solution is proposed. The problem of random distribution to random value is transformed to random vector to random value by…
A new approach is proposed for reconstruction of images from Radon projections. Based on Fourier expansions in orthogonal polynomials of two and three variables, instead of Fourier transforms, the approach provides a new algorithm for the…
In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…
Problems of interpolation, classification, and clustering are considered. In the tenets of Radon--Nikodym approach $\langle f(\mathbf{x})\psi^2 \rangle / \langle\psi^2\rangle$, where the $\psi(\mathbf{x})$ is a linear function on input…
The Radon-Nikodym theorem plays a significant role in the definition of Shannon entropy, f-divergences, and other basic quantities in information theory. The existence of Radon Nikodym derivates appear in many text books in measure theory…
The paper addresses the generalization of the half-quadratic minimization method for the restoration of images having values in a complete Riemannian manifold. We recall the half-quadratic minimization method using the notation of the…
We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability…
Image moments are weighted sums over pixel values in a given image and are used in object detection and localization. Raw image moments are derived directly from the image and are fundamental in deriving moment invariants quantities. The…
A set of orthonormal polynomials is proposed for image reconstruction from projection data. The relationship between the projection moments and image moments is discussed in detail, and some interesting properties are demonstrated.…
Radon transform is a type of transform which is used in image processing to transfer the image into intercept-slope coordinate. Its diagonal properties made it appropriate for some applications which need processes in different degrees.…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…
A simple model of near-field pixel-to-pixel image transfer using magneto-inductive arrays is presented. The response of N-dimensional rectangular arrays is first found as an excitation of eigenmodes. This analytical method involves…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
The aim of this note is to establish two Radon--Nikodym type theorems for nonnegative Hermitian forms defined on a real or complex vector space. We apply these results to prove the known Radon--Nikodym theorems of the theory of…
Several important classes of images such as text, barcode and pattern images have the property that pixels can only take a distinct subset of values. This knowledge can benefit the restoration of such images, but it has not been widely…
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…
Fourier ptychography microscopy (FPM) is a new computational imaging technique that can provide gigapixel images with both high resolution and a wide field of view (FOV). However, time consuming of the data-acquisition process is a critical…
Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We…