## Optimisation in Image Analysis

#### Collaborative filtering for the analysis of colour images

Most images can be approximated with high accuracy by an image with sparse representation in some basis. A representation is sparse if only a small number of coefficients in a linear combination are non-zero. The problem of optimal selection of the set of these non-zero coefficients is an optimisation problem in L_0 space. Very often, the solution to this difficult optimisation problem can be well approximated by a related optimisation problem in L_1 space. This problem is much simpler. In particular, the solution to this problem is a limit of a sequence of solutions of optimisation problems in L_2 space.

#### Efficient storage of images using sparse representations

Collaborative filtering is the process of filtering for information or patterns using techniques involving collaboration among multiple data sources. We apply these techniques for the analysis and efficient storage of colour images, which can be considered as a set of three highly correlated images.

#### Analysis of similarity of images using SSA techniques

Singular spectrum analysis (SSA) can be used for analysing not only time series but images too. Application of SSA to a set of images can be used for classification of images and identifying similar images (for example, images of the same person). We can also define a distance between images based on SSA-similarity between these images. First results show that SSA based classification of images often works better that the Support Vector Machines.

#### Cardiff investigators

- Prof Russell Davies
- Prof Alexander Balinsky
- Prof Anatoly Zhigljavsky
- Dr Andrey Pepelyshev
- Dr Valentina Moskvina

#### Collaborators

- Dr Vladimir Nekrutkin
- Dr Nina Golyandina
- Dr Licesio Rodriguez Aragon