Rakeness in the design of AnalogtoInformation Conversion of Sparse and Localized Signals
Abstract
Design of Random Modulation PreIntegration systems based on the restrictedisometry property may be suboptimal when the energy of the signals to be acquired is not evenly distributed, i.e. when they are both sparse and localized. To counter this, we introduce an additional design criterion, that we call rakeness, accounting for the amount of energy that the measurements capture from the signal to be acquired. Hence, for localized signals a proper system tuning increases the rakeness as well as the average SNR of the samples used in its reconstruction. Yet, maximizing average SNR may go against the need of capturing all the components that are potentially nonzero in a sparse signal, i.e., against the restricted isometry requirement ensuring reconstructability. What we propose is to administer the tradeoff between rakeness and restricted isometry in a statistical way by laying down an optimization problem. The solution of such an optimization problem is the statistic of the process generating the random waveforms onto which the signal is projected to obtain the measurements. The formal definition of such a problems is given as well as its solution for signals that are either localized in frequency or in more generic domain. Sample applications, to ECG signals and small images of printed letters and numbers, show that rakenessbased design leads to nonnegligible improvements in both cases.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 arXiv:
 arXiv:1205.1144
 Bibcode:
 2012arXiv1205.1144M
 Keywords:

 Computer Science  Information Theory;
 Computer Science  Computer Vision and Pattern Recognition
 EPrint:
 IEEE Transactions on Circuits and Systems, Part I, vol. 59, n. 5, pp. 10011014, 2012