Section: New Results

Statistical Learning and Bayesian Analysis

Prediction of Sequences of Structured and Unstructured Data

Statistical performance analysis of a fast super-resolution technique using noisy translations [38]

It is well known that the registration process is a key step for super-resolution reconstruction. In this work, we propose to use a piezoelectric system that is easily adaptable on all microscopes and telescopes for controlling accurately their motion (down to nanometers) and therefore acquiring multiple images of the same scene at different controlled positions. Then a fast super-resolution algorithm can be used for efficient super-resolution reconstruction. In this case, the optimal use of r2 images for a resolution enhancement factor r is generally not enough to obtain satisfying results due to the random inaccuracy of the positioning system. Thus we propose to take several images around each reference position. We study the error produced by the super-resolution algorithm due to spatial uncertainty as a function of the number of images per position. We obtain a lower bound on the number of images that is necessary to ensure a given error upper bound with probability higher than some desired confidence level.

Quantitative control of the error bounds of a fast super-resolution technique for microscopy and astronomy [11]

While the registration step is often problematic for super-resolution, many microscopes and telescopes are now equipped with a piezoelectric mechanical system which permits to ac-curately control their motion (down to nanometers). There-fore one can use such devices to acquire multiple images of the same scene at various controlled positions. Then a fast super-resolution algorithm [1] can be used for efficient super-resolution. However the minimal use of r 2 images for a resolution enhancement factor r is generally not sufficient to obtain good results. We propose to take several images at po-sitions randomly distributed close to each reference position. We study the number of images necessary to control the error resulting from the super-resolution algorithm by [1] due to the uncertainty on positions. The main result is a lower bound on the number of images to respect a given error upper bound with probability higher than a desired confidence level.

Statistical analysis of superresolution

A diffusion strategy for distributed dictionary learning [12]

We consider the problem of a set of nodes which is required to collectively learn a common dictionary from noisy measurements. This distributed dictionary learning approach may be useful in several contexts including sensor networks. Dif-fusion cooperation schemes have been proposed to estimate a consensus solution to distributed linear regression. This work proposes a diffusion-based adaptive dictionary learning strategy. Each node receives measurements which may be shared or not with its neighbors. All nodes cooperate with their neighbors by sharing their local dictionary to estimate a common representa-tion. In a diffusion approach, the resulting algorithm corresponds to a distributed alternate optimization. Beyond dictionary learn-ing, this strategy could be adapted to many matrix factorization problems in various settings. We illustrate its efficiency on some numerical experiments, including the difficult problem of blind hyperspectral images unmixing.