**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Person# John Paul Ward

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related units

Loading

Courses taught by this person

Loading

Related research domains

Loading

Related publications

Loading

People doing similar research

Loading

Related publications (32)

Loading

Loading

Loading

Related research domains (19)

Courses taught by this person

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy

White noise

In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, i

Stochastic process

In probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has

No results

Related units (1)

Julien René Fageot, Michaël Unser, John Paul Ward

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimation of the Besov regularity of Levy white noises and generalized Levy processes. We show in particular that non-Gaussian generalized Levy processes are more compressible in a wavelet basis than the corresponding Gaussian processes, in the sense that their n-term approximation errors decay faster. We quantify this compressibility in terms of the Blumenthal-Getoor indices of the underlying Levy white noise.

People doing similar research (110)

, , , , , , , , ,

, , , ,

The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated in the literature, and their localization and detection properties are well known. In this paper, we study the complementary topic of local orientation estimation, which has not received similar attention. Simply stated, the problem that we address is the following: estimate the angle of rotation of a pattern with steerable filters centered at the same location, where the image is corrupted by colored isotropic Gaussian noise. For this problem, we propose an estimator formulated as linear combinations of circular harmonics with given radial profiles. We prove that the proposed estimator is unbiased. This property allows us to use a statistical framework based on the Cramer-Rao lower bound (CRLB) to study the limits on the accuracy of the corresponding class of estimators. We aim at evaluating the performance of detection methods based on steerable filters in terms of angular accuracy (as a lower bound), while considering the connection to maximum likelihood estimation. Beyond the general results, we analyze the asymptotic behavior of the lower bound in terms of the order of steerablility and propose an optimal subset of components that minimizes the bound. We define a mechanism for selecting optimal subspaces of the span of the detectors. These are characterized by the most relevant angular frequencies. Finally, we project our template to the span of circular harmonics with given radial profiles and experimentally show that the prediction accuracy achieves the predicted CRLB. As an extension, we also consider steerable wavelet detectors.

, ,

A convolution algebra is a topological vector space X that is closed under the convolution operation. It is said to be inverse-closed if each element of X whose spectrum is bounded away from zero has a convolution inverse that is also part of the algebra. The theory of discrete Banach convolution algebras is well established with a complete characterization of the weighted l1 algebras that are inverse-closed-these are henceforth referred to as the Gelfand-Raikov-Shilov (GRS) spaces. Our starting point here is the observation that the space S(Zd) of rapidly decreasing sequences, which is not Banach but nuclear, is an inverse-closed convolution algebra. This property propagates to the more constrained space of exponentially decreasing sequences E(Zd) that we prove to be nuclear as well. Using a recent extended version of the GRS condition, we then show that E(Zd) is actually the smallest inverse-closed convolution algebra. This allows us to describe the hierarchy of the inverse-closed convolution algebras from the smallest, E(Zd), to the largest, l1(Zd). In addition, we prove that, in contrast to S(Zd), all members of E(Zd) admit well-defined convolution inverses in S '(Zd) with the unstable scenario (when some frequencies are vanishing) giving rise to inverse filters with slowly-increasing impulse responses. Finally, we use those results to reveal the decay and reproduction properties of an extended family of cardinal spline interpolants.