An Adaptive and Information Theoretic Method For Compressed Sampling

By considering an s-sparse signal x similar to (X, P) to be an instance of vector random variable X = (X-1, ... , X-n)(t) We determine a sequence of binary sampling vectors for characterizing the signal x and completely determining it from the samples. Unlike the standard approaches, ours is adaptive and is inspired by ideas from the theory of Huffman codes. The method seeks to minimize the number of steps needed for the sampling and reconstruction of any sparse vector x similar to (X, P). We prove that the expected total cost (number of measurements and reconstruction combined) that we need for an s-sparse vector in R-n is no more than s log n + 2s.