This paper is concerned with the logical structure of arithmetical the ories We survey results concerning logics and admissible rules of con structive arithmetical theories We prove a new theorem the admissible propositional rules of Heyting Arithmetic are the same as the admissible propositional rules of Intuitionistic Propositional Logic We provide some further insights concerning predicate l...

In this paper we consider the following separate but related questions: “How do we construct an effective admissible domain representation of a space X from a pseudobasis on X?”, and “How do we construct an effective admissible domain representation of the inductive limit of a directed system (Xi)i∈I of topological spaces, given effective admissible domain representations of the individual spac...

Wavelets and their associated transforms are highly efficient when approximating and analyzing onedimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient of sparsely approximating and also of analyzing in the sense of, for instance, detecting their direction. Shearlets are a directional repres...

This paper introduces a Parseval frame of shearlets for the representation of 3D data, which is especially designed to handle geometric features such as discontinuous boundaries with very high efficiency. This system of 3D shearlets forms a multiscale pyramid of well-localized waveforms at various locations and orientations, which become increasingly thin and elongated at fine scales. We prove ...

Synthetic Aperture Radar (SAR) images suffer of multiplicative speckle noise, which damages the radiometric resolution of SAR images and makes the data interpretation difficult. Bayesian shrinkage in a transformed domain is a well-known method based on finding threshold value to suppress the speckle noise. This paper present a new approach to obtain the optimum threshold values for Bayesian shr...

Convolutional Neural Networks (CNNs) are a type of deep neural network which have performed well at image and audio classification. One approach to understanding the success of CNNs is Mallat’s scattering transform, which formalizes the observation that the filters learned by a CNN have wavelet-like structure. The resulting transform generates a representation that is approximately translation ...

We consider the problem of estimating the scale parameter &beta of a rescaled F-distribution when &beta has a lower bounded constraint of the form &beta&gea, under the entropy loss function. An admissible minimax estimator of the scale parameter &beta, which is the pointwise limit of a sequence of Bayes estimators, is given. Also in the class of truncated linear estimators, the admissible estim...

let  $varpi$ be a representation of the homogeneous space $g/h$, where $g$ be a locally compact group and  $h$ be a compact subgroup of $g$. for  an admissible wavelet $zeta$ for $varpi$  and $psi in l^p(g/h), 1leq p