Publications related to Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

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Theoretical Framework for the Assessment of Uncertainties in Snow Depth Measurements

Michael Lehning, Ernesto Trujillo Gomez

In recent years, marked improvements in our knowledge of the statistical properties of the spatial distribution of snow properties have been achieved thanks to improvements in measuring technologies (e.g., LIDAR, TLS, and GPR). Despite of this, objective a ...

2014

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Correlation Estimation from Compressed Images

Pascal Frossard, Vijayaraghavan Thirumalai

This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We assume that the i ...

Elsevier2013

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Michaël Unser, Arash Amini, Emrah Bostan, Ulugbek Kamilov

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools fro ...

Ieee-Inst Electrical Electronics Engineers Inc2013

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

Michaël Unser, Philippe Thévenaz, Arash Amini, John Paul Ward

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 ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Linear Bayesian Reinforcement Learning

Christos Dimitrakakis, Nikolaos Tziortziotis

This paper proposes a simple linear Bayesian approach to reinforcement learning. We show that with an appropriate basis, a Bayesian linear Gaussian model is sufficient for accurately estimating the system dynamics, and in particular when we allow for corre ...

2013

Fast Dual Variational Inference for Non-Conjugate Latent Gaussian Models

Matthias Seeger, Mohammad Emtiyaz Khan

Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals in- volving the Gaussian prior and non-conjugate likelihoods. Algorithms based on variation ...

Omni Press2013

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Michaël Unser, John Paul Ward, Stamatios Lefkimmiatis

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 ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

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Theoretical Framework for the Assessment of Uncertainties in Snow Depth Measurements

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Correlation Estimation from Compressed Images

Compressed Optical Imaging

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

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

Linear Bayesian Reinforcement Learning

Fast Dual Variational Inference for Non-Conjugate Latent Gaussian Models

Hessian Schatten-Norm Regularization for Linear Inverse Problems

A fast Griffin Lim Algorithm

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

Theoretical Framework for the Assessment of Uncertainties in Snow Depth Measurements

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Compressed Optical Imaging

Linear Bayesian Reinforcement Learning

Fast Dual Variational Inference for Non-Conjugate Latent Gaussian Models

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Correlation Estimation from Compressed Images

Hessian Schatten-Norm Regularization for Linear Inverse Problems

A fast Griffin Lim Algorithm