# Adaptive Bat Algorithm Optimization Strategy for Observation Matrix
## 2 Related Works  
To analyze the influence of the observation matrix on the algorithm, five different observation matrices and two algorithm optimized observation matrices are used for reconstructing the signal. It includes the random Gaussian observation matrix [6], random Bernoulli observation matrix [9], singular value decomposition, mean optimization random Gaussian observation matrix [11], the observation matrix optimized by the standard bat algorithm, and the observation matrix optimized by the adaptive bat algorithm. The signal recovery, as an important process of compressed sensing, has an essential impact on reconstruction accuracy. Therefore, researchers have proposed many improvement strategies to improve the accuracy of signal recovery, which include the following four categories: (1) Greedy algorithm based on local search strategy [48; 49]; (2) convex optimization algorithm based on linear programming problem [50; 51]; (3) non-convex optimization algorithm based on linear programming problem [52; 53]; and (4) reconstruction algorithm based on natural heuristic algorithm [54; 55]. In the process of reconstruction [56], the signals can be compressed and sampled in real-time; moreover, the original signals also can be recovered by some specific reconstruction algorithms. Orthogonal matching pursuit algorithm (OMP) [57], due to its fast reconstruction velocity and simple implementation, is widely used in the field of compressed sensing. In this paper, the OMP algorithm is employed to optimize the observation matrix. Its process is as follows:1. Calculate the correlation coefficient between the sensing matrix (\(A_{CS}\)) and residual projection, and select the maximum correlation coefficient atomic as updated support sets. 2. Use the Schmidt orthogonalization processing for the sensing matrix to eliminate interference on subsequent atoms. 3. Least-square method is used to update residuals and obtain the reconstructed signals. The bat algorithm can obtain better results when solving continuous optimization problems. However, for a large number of discrete problems in practical engineering, it often tends to cause slow convergence and fall into local optimum. Therefore, discrete bat algorithms have been proposed. [PERSON] et al. [58] proposed a binary bat algorithm to deal with discrete problems and introduced a binary coding strategy to update the velocity and position of bats individuals. [PERSON] et al. [59] proposed a discrete bat algorithm and introduced Hamming code distance to enhance the ability to learn from optimal bats. [PERSON] et al. [60] applied the discrete bat algorithm to the flexible shop scheduling problem. To accelerate the convergence velocity of the algorithm, they also proposed to introduce the bat's position mutation strategy into the position update strategy and calculated the fitness value by using the clock algorithm. To jump out of the local extremum solution, [PERSON] et al. [61] introduced the Levy flight strategy and updated the speed and position of the individual by randomly increasing the step size. Different from the above work, [PERSON] et al. [62] directly used the Levy flight strategy to update the speed and position. In order to enhance the local search ability, [PERSON] et al. [63] proposed a novel variant of the bat algorithm based on global search and introduced a weighting factor. According to the requirements of numerical optimization problems, [PERSON] et al. [64] redefined the updated equation of velocity and position, and proposed an evolutionary bat algorithm, which makes the algorithm achieve higher accuracy in the optimization process. In addition, for multi-objective optimization problems, many multi-objective bat algorithms have been proposed. [PERSON] [65] proposed a multi-objective bat optimization algorithm (MOBA) to solve continuous optimization problems and introduced the weighted method into the algorithm. [PERSON] et al.