Abstract: Compressive sampling techniques can effectively reduce the acquisition costs of high-dimensional signals by utilizing the fact that typical signals of interest are often sparse in a certain domain.For compressive samplers,the number of samples needed to reconstruct a sparse signal is determined by the actual sparsity order of the signal.However,the actual sparsity order is often unknown or dynamically varying in practice,and the practical sampling rate has to be chosen conservatively according to an upper bound.To circumvent such wastage of the sampling resources,this paper introduces the concept of sparsity order estimation,which aims to accurately acquire the actual sparsity order prior to sparse signal recovery,by using a very small number of samples.A statistical learning methodology is used.Capitalizing on this gap,this paper also develops a two-step compressive spectrum sensing algorithm for wideband cognitive radios as an illustrative application.The first step quickly estimates the actual sparsity order of the wide spectrum of interest using a small number of samples,and the second step adjusts the total number of collected samples according to the estimated signal sparsity order.