Parallel Sampling and Reconstruction with Permutation in Multidimensional Compressed Sensing

The advent of compressed sensing provides a new way to sample and compress signals. In this thesis, a parallel compressed sensing architecture is proposed, which samples a twodimensional reshaped multidimensional signal column by column using the same sensing matrix. Compared to architectures that sample a vector-reshaped multidimensional signal, the sampling device in the parallel compressed sensing architecture stores a smaller-sized sensing matrix and has lower computational complexity. Besides, the reconstruction of the multidimensional signal can be conducted in parallel, which reduces the computational complexity and time for reconstruction at the decoder side. In addition, when parallel sampling is not required but analog compressed sensing is desired, an alternative architecture proposed in this thesis, named parallel compressed sensing reconstruction architecture, can be used. In both proposed architectures, permutation is introduced and shown to enable the reduction of the required number of measurements for a given desired reconstruction error performance.