相关论文: Easy-to-compute parameterizations of all wavelet f…

All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi…

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…

We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent…

In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…

Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…

The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…

We give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These…

In this manuscript a factor graph approach is employed to investigate the recursive filtering problem for a mixed linear/nonlinear state-space model, i.e. for a model whose state vector can be partitioned in a linear state variable…

We present a framework for the optimal filtering of spherical signals contaminated by realizations of an additive, zero-mean, uncorrelated and anisotropic noise process on the sphere. Filtering is performed in the wavelet domain given by…

We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…

Despite the remarkable success of deep learning in pattern recognition, deep network models face the problem of training a large number of parameters. In this paper, we propose and evaluate a novel multi-path wavelet neural network…

Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in…

A new parametrization (one-to-one onto map) of compact wavelet matrices of rank $m$ and of order and degree $N$ is proposed in terms of coordinates in the Euclidian space $R^{(m-1)N}$. The developed method depends on Wiener-Hopf…

Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…

This paper introduces factored conditional filters, new filtering algorithms for simultaneously tracking states and estimating parameters in high-dimensional state spaces. The conditional nature of the algorithms is used to estimate…

We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L^2 function, a given likelihood function has an alternative representation as a product of…

Square-root Kalman filters propagate state covariances in Cholesky-factor form for numerical stability, and are a natural target for gradient-based parameter learning in state-space models. Their core operation, triangularization of a…

Many continuous wavelets are defined in the frequency domain and do not have analytical expressions in the time domain. Meyer wavelet is ordinarily defined in this way. In this note, we derive new straightforward analytical expressions for…

We present a model for exact recursive Bayesian filtering based on lifted multiset states. Combining multisets with lifting makes it possible to simultaneously exploit multiple strategies for reducing inference complexity when compared to…