This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms. of structure from motion, or local coordinates where 3D points are represented, in which case we are dealing with a 3D point-set registration problem.More abstractly, the goal of the group synchronization problem [1, 2] is to recover elements of a group from noisy measures of their ratios. In our case, absolute angular attitudes R 1 , . . . , R n are elements of the Special Orthogonal Group SO (3), and relative attitudes R ij = R i R T j are their ratios. The same problem is analysed in depth in [3], under the name "multiple rotation averaging". Our solution to the rotation synchronization problem is inspired by recent advances in the fields of robust principal component analysis and matrix completion. The main and original contribution of this paper is the formulation of the rotation synchronization problem as a "low-rank and sparse matrix decomposition", by conceiving a novel cost function that naturally includes missing data and outliers in its definition. Secondly, we develop a minimization scheme for that cost function -called R-GoDec -that leverages on the GoDec algorithm [4]. The resulting method is robust, by construction, fast, thanks to the use of Bilateral Random Projections (BRP) in place of Singular Value Decomposition (SVD), and compact, as it consist of a single fixed point iteration that can be coded in a few lines of MATLAB. Most of all, the framework is modular, as -in principle -any low-rank and sparse decomposition method able to deal with outliers and missing data can replace R-GoDec.This paper is organized as follows. Applications of the rotation synchronization problem are presented in Section 2 while existing solutions are described in Section 3. Section 4 is an overview of the theoretical background required to define our algorithm, i.e. lowrank and sparse matrix decomposition. Section 5 defines the rotation synchronization problem. Section 6 provides a detailed description of our robust solution. The method proposed in this section is supported by experimental results on both synthetic and real data, shown in Section 7. The conclusions are presented in Section 8. This paper is an extended version of [5].

Abstract.Rijndael is the winner algorithm of the AES contest; therefore it should become the most used symmetric-key cryptographic algorithm. One important application of this new standard is cryptography on smart cards. In this paper we present an optimisation of the Rijndael algorithm to speed up execution on 32-bits processors with memory constraints, such as those used in smart cards. First a theoretical analysis of the Rijndael algorithm and of the proposed optimisation is discussed, and then simulation results of the optimised algorithm on different processors are presented and compared with other reference implementations, as known from the technical literature.

This paper deals with the synchronization problem, which arises in multiple 3D point-set registration and in structure-from-motion. The problem is formulated as a low-rank and sparse matrix decomposition that caters for missing data, outliers and noise, and it benefits from a wealth of available decomposition algorithms that can be plugged-in. A minimization strategy, dubbed R-GoDec, is also proposed. Experimental results on simulated and real data show that this approach o↵ers a good trade-o↵ between resistance to outliers and speed.

No abstract

In this paper, we deal with the localization problem in wireless sensor networks, where a target sensor location must be estimated starting from few measurements of the power present in a radio signal received from sensors with known locations. Inspired by the recent advances in sparse approximation, the localization problem is recast as a block-sparse signal recovery problem in the discrete spatial domain. In this paper, we develop different RSS-fingerprinting localization algorithms and propose a dictionary optimization based on the notion of the coherence to improve the reconstruction efficiency. The proposed protocols are then compared with traditional fingerprinting methods both via simulation and on-field experiments. The results prove that our methods outperform the existing ones in terms of the achieved localization accuracy.