Publications by John Paul Ward

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Bayesian estimation problems involving Gaussian distributions often result in linear estimation techniques. Nevertheless, there are no general statements as to whether the linearity of the Bayesian estimator is restricted to the Gaussian case. The two comm ...

We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and sto ...

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. ...

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which a ...

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters fr ...

Motivated by the interior tomography problem, we propose a method for exact reconstruction of a region of interest of a function from its local Radon transform in any number of dimensions. Our aim is to verify the feasibility of a one-dimensional reconstru ...

In this work, we investigate the relationship between continuous-time autoregressive (AR) models and their sampled version. We consider uniform sampling and derive criteria for uniquely determining the continuous-time parameters from sampled data; the mode ...

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 ...

Motivation: SpotCaliper is a novel wavelet-based image-analysis software providing a fast automatic detection scheme for circular patterns (spots), combined with the precise estimation of their size. It is implemented as an ImageJ plugin with a friendly us ...

We consider the problem of sampling continuous-time auto-regressive processes on a uniform grid. We investigate whether a given sampled process originates from a single continuous-time model, and address this uniqueness problem by introducing an alternativ ...

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform indepe ...

In this paper, we study the Besov regularity of Levy white noises on the d-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results for gene ...

The Riesz transform is a natural multidimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. More recently, the Riesz transform and its variants have been used to construc ...

It is known that a Green's function-type condition may be used to derive rates for approximation by radial basis functions (RBFs). In this paper, we introduce a method for obtaining rates for approximation by functions which can be convolved with a finite ...

To address the classic interior tomography problem where projections at each view extend only to the shadow of a circular region completely interior to the subject being scanned, previously we showed that the exact recovery of two- and three-dimensional pi ...

We define and investigate the Local Rotation Invariance (LRI) and Directional Sensitivity (DS) of radiomics features. Most of the classical features cannot combine the two properties, which are antagonist in simple designs. We propose texture operators bas ...

In this paper, we construct compactly supported radial basis functions that satisfy optimal approximation properties. Error estimates are determined by relating these basis functions to the class of Sobolev splines. Furthermore, we derive new rates for app ...

John Paul Ward

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On the Linearity of Bayesian Interpolators for Non-Gaussian Continuous-Time AR(1) Processes

Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling

Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Divergence-Free Wavelet Frames

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

Angular Accuracy of Steerable Feature Detectors

SpotCaliper: Fast Wavelet-Based Spot Detection with Accurate Size Estimation

Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?

Optimized Kaiser-Bessel Window Functions for Computed Tomography

On the Besov regularity of periodic Levy noises

Decay Properties of Riesz Transforms and Steerable Wavelets

L (p) error estimates for approximation by Sobolev splines and Wendland functions on a"e (d)

Interior Tomography Using 1D Generalized Total Variation. Part II: Multiscale Implementation

Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

Approximation Properties Of Sobolev Splines And The Construction Of Compactly Supported Equivalents