Related papers: Complex-order Derivative and Integral Filters and …

The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…

Second order intensity correlations of speckle illumination are extensively used in imaging applications that require going beyond the Rayleigh limit. The theoretical analysis shows that significantly improved imaging can be extracted from…

Deep models have been widely and successfully used in image manipulation detection, which aims to classify tampered images and localize tampered regions. Most existing methods mainly focus on extracting global features from tampered images,…

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…

Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the…

The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…

In this paper, we design two fundamental differential operators for the derivation of rotation differential invariants of images. Each differential invariant obtained by using the new method can be expressed as a homogeneous polynomial of…

The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual…

We investigate higher-dimensional $\Delta$-systems indexed by finite sets of ordinals, isolating a particular definition thereof and proving a higher-dimensional version of the classical $\Delta$-system lemma. We focus in particular on…

The goal of image ordinal estimation is to estimate the ordinal label of a given image with a convolutional neural network. Existing methods are mainly based on ordinal regression and particularly focus on modeling the ordinal mapping from…

This paper proposes a generic method to learn interpretable convolutional filters in a deep convolutional neural network (CNN) for object classification, where each interpretable filter encodes features of a specific object part. Our method…

The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…

In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the…

One issue with computer based histopathology image analysis is that the size of the raw image is usually very large. Taking the raw image as input to the deep learning model would be computationally expensive while resizing the raw image to…

We present differentiable particle filters (DPFs): a differentiable implementation of the particle filter algorithm with learnable motion and measurement models. Since DPFs are end-to-end differentiable, we can efficiently train their…

A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations…

Complex-valued neural networks (CVNNs) are nonlinear filters used in the digital signal processing of complex-domain data. Compared with real-valued neural networks~(RVNNs), CVNNs can directly handle complex-valued input and output signals…

To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…

Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF)…

Neural network compression empowers the effective yet unwieldy deep convolutional neural networks (CNN) to be deployed in resource-constrained scenarios. Most state-of-the-art approaches prune the model in filter-level according to the…