Sparse Wavelet Transform for Underwater Acoustic Image Compressed Sensing

Sonar plays a very important role in underwater detection and exploration. Sonar images can show the underwater scene which are transmitted through the underwater acoustic (UWA) channel. However, the UWA channel is challenging to transmit images because of the characteristics of the channel, such as doppler spread, multipath effect, and especially limited bandwidth. In order to transmit images efficiently, in recent years, compressed sensing (CS) has been widely used as an image compressed method. The sparse representation in CS can be performed by the wavelet transform and other transforms which can generate sparse signal. In this paper, a novel signal transform called sparse wavelet transform (SWT) is proposed to find the most sparse representation of signal. The proposed algorithm can transmit sonar images with less data and thus improve the bandwidth utilization. Sparse wavelet transform is compared with Bandelets transform and wavelet transform in an experiment. The results show that the peak signal to noise ratio (PSNR) and the structural similarity (SSIM) index of sparse wavelet transform are higher than that of wavelet transform and Bandelets transform at the same sample rate.