The Wavelet Compressibility of Compound Poisson Processes

In this paper, we precisely quantify the wavelet compressibility of compound Poisson processes. To that end, we expand the given random process over the Haar wavelet basis and we analyse its asymptotic approximation properties. By only considering the nonzero wavelet coefficients up to a given scale, what we call the greedy approximation, we exploit the extreme sparsity of the wavelet expansion th...