### Introduction

The face recognition problem has been widely studied in the last decades. This interest is motivated by the numerous applications it involves, such as human- computer interaction (HCI), content-based image retrieval (CBIR), security systems and access control systems. Unfortunately most of the existing methods behave very well under controlled conditions, but their performance drop down significantly when dealing with uncontrolled conditions. The term uncontrolled conditions refers to several problems affecting the images, including variations in the environmental conditions (lighting, clutter background), variations in the acquired face (expressions, poses, occlusions), and even the quality of the acquisition (focus/blurred). All these problems have high probability to happen in real applications, thus they need to be faced to have a robust face recognition system (FRS).

### Sparse representation in LDA space

We design a FRS, namely the k-LiMapS_HFR, which faces in a novel way the above mentioned hurdles. It is a holistic sparse representation method that, after having automatically cropped the face images and projected them in the LDA space, attains the sparse solution adopting the $\ell_0$- pseudonorm optimization called k-LiMapS. Such sparse search method is based on a suitable parametric family of Lipschitzian type mappings providing an easy and fast iterative schema. Projecting the images in the LDA space and replacing the original simplex method used in with k-LiMapS, the classification method becomes much faster, and achieves higher performance in presence of both unregistered, uncontrolled images, and poor dictionaries (i.e. with only few images per subject). The diagram representing the FRS is illustrated in Fig. 1.

### References

1) A. Adamo, G. Grossi, R. Lanzarotti, and J. Lin. Robust face recognition using sparse representation in LDA space. Machine Vision and Applications, 1-11. 2015.
2) G. Grossi, R. Lanzarotti, J. Lin. A Selection Module for Large-Scale Face Recognition Systems. In Image Analysis and Processing - ICIAP 2015. Lecture Notes in Computer Science, 9280, p. 529-539, 2015.
3) A. Adamo, G. Grossi, and R. Lanzarotti. Face Recognition in Uncontrolled Conditions Using Sparse Representation and Local Features. In Image Analysis and Processing - ICIAP 2013 - 17th International Conference, p. 31-40, 2013.
4) A. Adamo, G. Grossi, and R. Lanzarotti. Local features and sparse representation for face recognition with partial occlusions. In IEEE International Conference on Image Processing, ICIP 2013, p. 3008-3012, 2013.