Performance improvement of the Compressive Classifier using equi-norm tight frames

Classifying sparse signals with compressive measurements is different from the well-known sparse recovery, for its focus is minimizing the probability of false classification rather than error of recovery. This paper considered the way to decrease the probability of false classification for compressive classifier. It is proved rigorously that the probability of false classification could be reduced by tightening the measurement matrix, that is, to simply make it row-orthogonal. As is known, equiangular tight frame (ETF) is the best choice in Comressive Classification for measurement matrix because of its optimal worst-case performance. But its existence and construction is problematic for some dimensions. So our results provided a convenient approach to improve the performance of compressive classifiers - The tightened measurement matrices could be better than before. Numerical results illustrated the validity of our conclusion.