AbstructWe investigate a very general subset of 2-D, orthogonal, compactly supported wavelets. This subset includes all the wavelets with a corresponding wavelet (polyphase) matrix that can be factored as a product of factors of degree-1 in one variable. In this paper, we consider, in particular, wavelets with vanishing moments. The number of vanishing moments that can be aichieved increases wi...

This work presents a multiscale framework to solve an inverse reinforcement learning (IRL) problem for continuous-time/state stochastic systems. We take advantage of a diffusion wavelet representation of the associated Markov chain to abstract the state space. This not only allows for effectively handling the large (and geometrically complex) decision space but also provides more interpretable ...

Many machine learning data sets are embedded in high-dimensional spaces, and require some type of dimensionality reduction to visualize or analyze the data. In this paper, we propose a novel framework for multiscale dimensionality reduction based on diffusion wavelets. Our approach is completely data driven, computationally efficient, and able to directly process non-symmetric neighborhood rela...

This paper presents a construction of compactly supported biorthogonal spline wavelets in L2(IR ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets from box splines of increasing smoothness is provided. Several examples are given to illustrate the method. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines,...

We introduce an object recognition system, based on generalized Gabor wavelets, called banana wavelets. In addition to the qualities frequency and orientation, banana wavelets have the attributes curvature and size. Banana wavelets can be metrically organized, a sparse and ef-cient representation of objects is learned utilizing this metric.

This paper deals with Chebyshev wavelets. We analyze their properties computing Fourier transform. Moreover, we discuss the differential of wavelets due to connection coefficients. Uniform convergence and approximation error allow us provide rigorous proofs. In particular, expand mother wavelet in Taylor series an application both fractional calculus fractal geometry. Finally, give two examples...