By leveraging the concept of signal sparsity, the new signal acquisition paradigm Compressive Sensing (CS) has successfully shifted the system complexity of the encoder to the decoder. If consideration must be given to solving the heavy decoding work while guaranteeing the privacy of the signal, one of the best choices is to outsource the sparse reconstruction service to a cloud with abundant computing resources. We propose to outsource sparse reconstruction service to multi-clouds in parallel with an assumption that multi-clouds cannot collude with each other in private. The owner protects the 2D signals' support-set, a set consisting of the indices of the nonzero entries in that signal, using a simple exchange primitives with low complexity and less memory rather than a full random permutation matrix. When carrying out parallel compressive sensing, this exchange primitive is equivalent to random permutation matrix, thus relaxing the RIP for 2D sparse signals with high probability. Then, the compressive measurements and support-set are distributed over multi-clouds for storage and reconstruction service. Each cloud only has a small amount of information of both the measurements and asymmetric support-set, therefore, the privacy of the original signal can be guaranteed.