  Detecting or classifying already known sparse signals contaminated by
Gaussian noise from compressive measurements is different from reconstructing
sparse signals, as its objective is to minimize the error probability which
describes performance of the detectors or classifiers. This paper is concerned
about the performance improvement of a commonly used Compressive Classifier. We
prove that when the arbitrary sensing matrices used to get the Compressive
Measurements are transformed into Equi-Norm Tight Frames, i.e. the matrices
that are row-orthogonal, The Compressive Classifier achieves better
performance. Although there are other proofs that among all Equi-Norm Tight
Frames the Equiangular tight Frames (ETFs) bring best worst-case performance,
the existence and construction of ETFs on some dimensions is still an open
problem. As the construction of Equi-Norm Tight Frames from any arbitrary
matrices is very easy and practical compared with ETF matrices, the result of
this paper can also provide a practical method to design an improved sensing
matrix for Compressive Classification. We can conclude that: Tight is Better!
