Johnathan M. Bardsley

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We consider a large-scale convex minimization problem with nonnegativity constraints that arises in astronomical imaging. We develop a cost functional which incorporates the statistics of the noise in the image data and Tikhonov regularization to induce stability. We introduce an efficient hybrid gradient projection-reduced Newton (active set) method. By(More)
We consider the problem of solving ill-conditioned linear systems Ax = b subject to the nonnegativity constraint x ≥ 0, and in which the vector b is a realization of a random vector b̂, i.e. b is noisy. We explore what the statistical literature tells us about solving noisy linear systems; we discuss the effect that a substantial black background in the(More)
In image processing applications, image intensity is often measured via the counting of incident photons emitted by the object of interest. In such cases, image data-noise is accurately modeled by a Poisson distribution. This motivates the use of Poisson maximum likelihood estimation for image reconstruction. However, when the underlying model equation is(More)
We consider a large-scale optimization problem with nonnegativity constraints that arises in an application of phase diversity to astronomical imaging. We develop a cost function that incorporates information about the statistics of atmospheric turbulence, and we use Tikhonov regularization to induce stability. We introduce an efficient and easily(More)
The noise contained in data measured by imaging instruments is often primarily of Poisson type. This motivates, in many cases, the use of the Poisson likelihood functional in place of the ubiquitous least squares data fidelity when solving image deblurring problems. We assume that the underlying blurring operator is compact, so that, as in the least squares(More)
In this paper, we present an algorithm for the restoration of images with an unknown, spatially-varying blur. Existing computational methods for image restoration require the assumption that the blur is known and/or spatially-invariant. Our algorithm uses a combination of techniques. First, we section the image, and then treat the sections as a sequence of(More)
The connection between Bayesian statistics and the technique of regularization for inverse problems has been given significant attention in recent years. For example, Bayes’ Law is frequently used as motivation for variational regularization methods of Tikhonov type. In this setting, the regularization function corresponds to the negative-log of the prior(More)
The earth’s atmosphere is not a perfect media through which to view objects in outerspace; turbulence in the atmospheric temperature distribution results in refractive index variations that interfere with the propagation of light. As a result, wavefronts are non-planar when they reach the ground. The deviation from planarity of a wavefront is known as phase(More)
The efficacy, safety, and tolerability of a moderate dose, 3-drug lipid-lowering regimen were evaluated among 29 male patients with hyperlipidemia and coronary artery disease. In an initial 12-month phase, regular niacin, 500 mg qid, lovastatin, 20 mg bid, and colestipol, 10 g/bid, were given with dose adjustment for lipid targets and side effects. This was(More)
High-dimensional inverse problems present a challenge for Markov chain Monte Carlo (MCMC)-type sampling schemes. Typically, they rely on finding an efficient proposal distribution, which can be difficult for large-scale problems, even with adaptive approaches. Moreover, the autocorrelations of the samples typically increase with dimension, which leads to(More)