Abstract
Aiming at the shortcomings of being rough by using the l1 norm to replace the original signal for signal reconstruction, this paper first constructs the l1 norm's smooth approximation function and studies the monotonicity and convergence of the optimal solution sequence. Second, the pseudo-function ||x||p (0 < p < 1) replaces ||x||1 in signal reconstruction, and the maximum entropy function is used to smooth lp (0 < p < 1). In this paper, the algorithm's performance is analyzed and its feasibility is verified using one- and two-dimensional signal reconstruction. This algorithm has smaller error than other compression reconstruction algorithms, better structure, and a more convenient calculation.
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