We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For such constraints, the associated projection...

This article proposes a new approach for computing a semi-explicit form of the solution to a class of Hamilton–Jacobi (HJ) partial differential equations (PDEs), using control techniques based on viability theory. We characterize the epigraph of the value function solving the HJ PDE as a capture basin of a target through an auxiliary dynamical system, called “characteristic system”. The propert...

This papers deals with the restoration of images corrupted by a non-invertible or ill-conditioned linear transform and Poisson noise. Poisson data typically occur in imaging processes where the images are obtained by counting particles, e.g., photons, that hit the image support. By using the Anscombe transform, the Poisson noise can be approximated by an additive Gaussian noise with zero mean a...

All things that live long are gradually so saturated with reason that their origin in unreason becomes improbable.. .. Does the good historian not, at bottom, contradict? —Friedrich Nietzsche, Daybreak We changed " extract " in the first page of the article to " epigraph. " Please check. Precisely because the experience of the 2001 HOPE conference was a bit unnerving, I want to start out with a...

This poem was written for the University of Otago 2020 ‘Writer’ competition, and awarded first place (Staff Poetry category) by judge Dr. Sue Wootten. The responds to competition prompt ‘Only Connect…’, which is epigraph from E. M. Forster’s novel, Howards End (1910). Given this prompt, given timing (shortly after New Zealand’s major national COVID-19 lockdown), I aimed use poetic language meta...

This article aims at the safety-critical control synthesis of network systems such that satisfaction safety constraints can be guaranteed. To handle large state dimension systems, an assume-guarantee contract is used to break problem into smaller subproblems. Parameterized signal temporal logic (pSTL) formally describe behaviors subsystems which we use as template for contract. We show robust i...

Proximal Markov chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize use nondifferentiable priors in statistics. Existing formulations proximal MCMC, however, require hyperparameters regularization parameters to be prespecified. In this article, we extend paradigm MCMC through introducing new class called e...