A Fast Algorithm of Compressed Sensing for 2D Signals

ABSTRACT Compressed sensing (CS) is a new signal acquisition method that can do sampling and compression of signals simultaneously. In order to reduce the signal reconstruction time of CS algorithms and lower the growth rate of the reconstruction time when increasing the size of signals, this paper proposes the algorithm of block whole orthogonal matching pursuit (BWOMP), which is a fast CS algorithm based on the method of orthogonal matching pursuit (OMP) for two-dimension (2D) signals. BWOMP defines a measurement parameter named whole-correlation. At each iteration, instead of computing the correlation between each atom and 1D residuals, the whole-correlation is computed as the correlation between the atom and the 2D residuals. After that, an approximation of the 2D signal is generated directly by BWOMP. By reducing the number of the iterations, this method can significantly lower the computational complexity. On the other hand, BWOMP introduces the concept of block compressed sensing (BCS), and redesigns the block size and the observation matrix. BCS reduces the consumption of computational resources (i.e. memory and CPU cycles) by reducing the size of variables (especially the matrixes). The experimental comparisons show that, in comparison with OMP, BWOMP can save at least 80% reconstruction time, which makes the increasing rate of reconstruction time linear. The results indicate that the proposed algorithm may have great performance advantage for complex cases.

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