Toward Sparse Planar Array Underwater Acoustical Imaging Using Compressive Sensing Pattern Matching Technique

3-D underwater acoustical imaging is an emerging technology used for ocean exploration and underwater vehicle navigation. Achieving high-resolution 3-D imaging is challenging due to the requirement of a substantial number of sensor elements, resulting in both computational and hardware complexities. A practical solution to this issue is the utilization of sparse arrays, which can exhibit performance akin to that of uniform arrays. Although designing sparse arrays for narrowband signals is relatively straightforward, designing sparse arrays for wideband signals, which is typically employed in imaging sonars, is challenging due to the frequency-dependent variation in the array response. In this work, an efficient and low complex approach is proposed for creating sparse wideband arrays with a frequency-dependent array response. The methodology employs the multitask Bayesian compressive sensing (MTBCS) algorithm to determine the minimum number of sparse sensor locations and weights with a minimum level of $l_{2}$ norm pattern matching error between the desired pattern and the pattern synthesized by the estimated weights. Compared to conventional narrowband design methods and least-squares solutions, this approach offers comparable sparsity with a minimum mean square error (mse). It can be applied to obtain frequency-dependent or frequency-invariant patterns for wideband signals. The performance of the proposed algorithm is demonstrated through various numerical simulations and experiments through the reconstruction of 2-D images of different underwater targets using uniform and sparse linear arrays. The proposed method has achieved up to 90.8% element saving for the test cases.