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This paper demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems. [ABSTRACT FROM AUTHOR]

A description of optimal sequences for direct-spread code-division multiple access (S-CDMA) is a byproduct of recent characterization of the sum capacity. This correspondence restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite-step algorithms from matrix theory. It proposes a new one-sided algorithm that is numerically stable and faster than previous methods. [ABSTRACT FROM AUTHOR]