Sparse signal representations have gained extensive study in recent years. In applications, there are large amounts of signals that are structured. Motivated by signal decomposition and scattered data reconstruction applications, we consider a particular type of structured signals which can be represented by a union of several sparse vectors. We define this type of signal as piecewise sparse signals. To find a piecewise sparse representation of a signal, we propose a thresholding version of piecewise orthogonal matching pursuit(TP OMP), which aims to overcome the disadvantages of P_OMP. We also establish the connection of piecewise sparsity and sampling over a union of subspaces. We evaluate the performance of the proposed greedy programs through simulations on surface reconstruction.