This work extended sparse decomposition (SD) into quaternion space in order to find a better sparse representation for acoustic vector array (AVA). A novel sparse decomposition algorithm based on the well-known orthogonal matching pursuit (OMP) for quaternionic signals was proposed and it was used to solve the question of direction of arrival (DOA) estimation of AVA in small snapshot number, coherent signal source and low signal noise ratio (SNR) case. Compare with the complex field SD algorithm, The results illustrate that the atomic length of the over-complete dictionary is reduced to one-third of that from the long vector model, while errors in DOA estimation are effectively eliminated using the long vector method when the true angles of DOA estimation lie within 1°. Simulation results verify the validity of this algorithm.