The particularity of the underwater acoustic channel has put forward a higher request for collection and efficient transmission of the underwater image. In this paper, based on the characteristics of sonar image, wavelet transform is used to sparse decompose the image, and selecting Gaussian random matrix as the observation matrix and using the orthogonal matching pursuit (OMP) algorithm to reconstruct the image. The experimental result shows that the quality of the reconstruction image and PSNR have gained great ascension compared to the traditional compression and processing of image based on the wavelet transform while they have the same measurement numbers in the coding portion. It provides a convenient for the sonar image’s underwater transmission.

Compressed Sensing(CS) can project a high dimensional signal to a low dimensional signal by a random measurement matrix . As the projection calculation is time-consuming in the process of reconstruction, the reconstruction speed is greatly affected.In order to improve the reconstruction speed , some improvement in the selection of the measurement matrix and the design of the reconstruction algorithm is made. The wavelet transform is used to sparse decompose the image, and the very sparse random projection matrix is used as the measurement matrix, after the image block processing we use the OMP algorithm to reconstruct the image. The experimental result shows that this method could reduce the algorithm time and improved the reconstruction speed greatly.

Compressive Sensing (CS) Theory enables sampling discrete signals with quite lower sampling rate compared with traditional Nyquist sampling rate and guaranteeing faithful reconstruction. Based on CS theory, Analog-to-Information Conversion (AIC) was proposed to process continuous-time signal. In this paper, the framework of Analog-to-Information Converter is composed by a pseudo-random demodulator, a low pass analog filter and a low speed sampler. And we mainly discuss the damage on the signal recovery produced by lower and higher orders of filter impulse response.