# Adaptive Bat Algorithm Optimization Strategy for Observation Matrix
## 1 Introduction  
With signals, images and video data are gradually increasing in contemporary life. To reduce the cost of data storage, transmission and processing, signals are often represented with less storage space at an acceptable level of distortion. Compressed sensing, as a technique for finding sparse solutions of underdetermined linear systems, is widely used in many fields, such as image processing, medical imaging, computer science, signal processing. Particularly, compressed sensing is used in signal processing to obtain and reconstruct sparse or compressible signals. For example, studies [1; 2; 3; 4] have shown that it is feasible to directly obtain a compressed representation with a variety of assumptions. The sparse observation matrix plays an important role in the reconstruction algorithm. In [5], [PERSON] et al. expounded the advantages of the compressed sensing theory in solving the problem of information redundancy for the traditional signal acquisition process. They analyzed the construction of the compressed sensing measurement matrix from four aspects. [PERSON] et al. [6] proposed a method for linear measurement of a given vector and returned it to the Euclidean accuracy range. Moreover, they suggested that the observation matrix should satisfy the restricted isometry property (RIP), andthe random Gaussian matrix was employed as the usual observation matrix. Then, the discriminant rules of the observation matrix and the sparse representation transformation basis were proposed by [PERSON] et al. [7]. [PERSON] et al. [8] took advantage of the tail boundedness of the sub-Gaussian distribution to design the sub-Gaussian distribution sparse observation matrix. [PERSON] et al. [9] revealed the relationship between the random Bernoulli matrix and the restricted isometry property (RIP) criterion. And to reduce storage space, [PERSON] [10] designed a Toeplitz matrix in the RIP criterion, which was generated by a single row vector loop. The random Gaussian observation matrix is an important method in the reconstruction process, which has received much attention and shown some advantages. [PERSON] et al. [11] decomposed the observation matrix by using singular value and increased the observation matrix independence of each column by adopting the mean value improvement strategy. [PERSON] et al. [12] proposed the evaluation index between the observation matrix and transform basis, and used the eigenvalue decomposition method to optimize the random Gaussian observation matrix. [PERSON] et al. [13] proposed the Gram matrix to make the observation matrix close to the unit matrix by optimizing iteration. [PERSON] et al. [14] used a gradient descent method to convert the Gram matrix to the unit matrix. And in order to reduce the correlation between the observation matrix and the transform basis, the orthogonal triangulation (QR) decomposition was proposed. According to the characteristics of the MIMO radar signal, [PERSON] et al. [15] optimized the signal-to-interference ratio and reduced the correlation and noise. In recent years, a large number of bio-inspired optimization algorithms have been proposed, such as the genetic algorithm (GA) [16; 17], but algorithm (BA) [18; 19; 20; 21], differential evolution (DE) [20; 21], firefly algorithm (FA) [22], artificial bee colony (ABC) [23; 24], cuckoo algorithm (CS) [25; 26; 27], and so on [28; 29; 30; 31; 32], which have been applied to various fields, including the optimization problems [33; 34; 35; 36; 37], practical application problems [38; 39; 40; 41], LEACH (Low Energy Adaptive Clustering Hierarchy) protocol optimization [42], and so on [43; 44; 45; 46]. Particularly, [PERSON] et al. [47] designed an optimization method based on the bat algorithm to optimize the random Gaussian observation matrix and reduced the reconstruction error. The remainder of this paper as follows. Section 2 gives an overview of the related work and our motivations. Section 3 introduces the proposed adaptive bat algorithm (ABA) in detail and indicates the specific method flow.