Improvement in accuracy for dimensionality reduction and reconstruction of noisy signals. Part II: The case of signal samples

In this paper, a novel interpretation of the problem of dimensionality reduction and reconstruction of random signals is studied. The problem and its solution target highly noisy signals and are considered in terms of signal samples. The solution is given by an iteration procedure where, on each iteration, solution parameters are optimally determined from the minimization of an associated cost function. The associated error diminishes with the increase in the number of iterations. The advantages of the considered technique are discussed and illustrated numerically.