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Permutation Enhanced Parallel Reconstruction with A Linear Compressive Sampling Device

In this letter, a permutation enhanced parallel reconstruction architecture for compressive sampling is proposed. In this architecture, a measurement matrix is constructed from a block-diagonal sensing matrix and the sparsifying basis of the target signal. In this way, the projection of the signal onto the sparsifying basis can be divided into several segments and all segments can be reconstructed in parallel. Thus, the computational complexity and the time for reconstruction can be reduced significantly. This feature is especially appealing for big data processing. Furthermore, to reduce the number of measurements needed to achieve the desired reconstruction error performance, permutation is introduced for the projection of the signal. It is shown that the permutation can be performed implicitly by using a pre-designed measurement matrix. Thus, the permutation enhanced parallel reconstruction can be achieved with a linear compressive sampling device.