# An ADS-Based Sparse Optimization Method for Sonar Imaging Sensor Arrays
## 1 Introduction  
Sonar imaging is widely used for underwater detection applications, such as military defense, engineering maintenance, accident rescue, topographic survey, and so on [1]. A variety of array sensor systems play an important role in sonar imaging. The conventional underwater array imaging systems generally include two main forms: front-view or side-scan sonar imaging. Both imaging approaches employ a one-dimensional (ID) linear array sensor to obtain two-dimensional (2D) imaging, and then further to get three-dimensional (3D) imaging [2]. Recently, a sonar imaging approach with a 2D array sensor has been in use, which adopts a subarray system and implements a multibeam technique. However, the imaging quality based on the subarray system is related to the number of subarrays and array elements. The higher the imaging quality, the more subarrays and array elements are required. This results in a very complex imaging system and increased manufacturing cost. One of the ways to solve this contradiction is to use sparse array sensor and synthetic aperture imaging technology. The first task is to design a sparse layout of array sensor elements while maintaining beam performance and imaging quality [3]. The sparse layout optimization of the sonar array sensor resembles that of a radar array antenna. Therefore, sparse methods for the sonar array sensor can be developed from the sparse radar array antenna [4]. These methods are mainly divided into two categories: random and determined. For the random methods, the distribution characteristics of beam response can be utilized in sparseoptimization. [PERSON] employed an improved genetic algorithm (GA) to obtain 2D sparse planar arrays, in which he established an optimization model with the goal of minimizing the peak side lobe level (PSLL). This method not only provides a specific sparse ratio of the array elements, but also maintains the array performance [5]. [PERSON] used the simulated annealing algorithm (SAA) to synchronously optimize the locations and the weighting coefficients of linear array elements when the side lobe of the beam pattern meets the relevant requirements [6]. The Convex Optimization (CO) method proposed by [PERSON] can globally optimize the positions and weighting coefficients of the array elements to obtain the maximal thinned array, and effectively reduce the computational complexity and PSLL values [7]. For a rectangular array with unequal amplitude excitation, [PERSON] employed the improved Particle Swarm Optimization (PSO) algorithm to perform sparse optimization of the array, in which the inertia weighting strategy is utilized for the global optimal particle perturbation and hopping. The improved algorithm greatly improves the convergence speed and accuracy [8]. The random array optimization algorithms are implemented repeatedly in the iterative search strategy to achieve one global optimal solution under constrained conditions. However, the common disadvantage of the random methods is the huge computational workload and the lack of real-time capacity in practical applications. [PERSON] proposed a low-complexity cross-type array, in which the multifrequency (MF) emission and parallel subarray (PS) beam-forming algorithms are used. The obtained sparse array can greatly bring down the hardware cost and complexity of the imaging system [9]. This scenario uses the Cyclic Difference Set (CDS) to perform sparse optimization on Multiple Inputs and Multiple Outputs (MIMO) arrays. The CDS method can obtain the prior estimates of PSLL and the position of array elements. However, this method cannot provide a solution to those arrays with an arbitrary aperture size due to the binary property of the autocorrelation function of the CDS [10]. [PERSON] adopted the Almost Difference Set (ADS) to perform sparse optimization of MIMO uniform linear arrays. The ADS method can determine the position of each array element of the transmit array and receive array, and perform a prior estimation on the side-lobe level of the beam pattern.