Geometric Constraints in Sensing Matrix Design for Compressed Sensing

Compressed Sensing (CS) has been proposed as a method able to reduce the amount of data needed to represent sparse signals. Nowadays, different approaches have been proposed in order to increase the performance of this technique in each stage that composes it. Particularly, this paper provides a critical review of the state-of-the art of some CS adaptations in the sensing stage to identify the strengths and limitations of each of them. In addition, a new method is proposed (Nearly Orthogonal Rakeness-based CS) that aims to overcome limits of the CS adaptations covered in this work. After intensive numerical simulations on synthetic signals and electroencephalographic (EEG) signals, the proposed approach outperforms discussed state-of-the-art approaches in terms of compression capability required to achieve a target quality of service.