Abstract The accurate reconstruction of a signal within a reasonable period is the key process that enables the application of compressive sensing in large-scale image transmission. The sparsity adaptive matching pursuit (SAMP) algorithm does not need prior knowledge on signal sparsity and has high reconstruction accuracy but has low reconstruction efficiency. To overcome the low reconstruction efficiency, we propose the use of the fast sparsity adaptive matching pursuit (FSAMP) algorithm, where the number of atoms selected in each iteration increases in a nonlinear manner instead of undergoing linear growth. This form of increase reduces the number of iterations. Furthermore, we use an adaptive reselection strategy in the proposed algorithm to prevent the excessive selection of atom. Experimental results demonstrated that the FSAMP algorithm has more stable reconstruction performance and higher reconstruction accuracy than the SAMP algorithm.
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