Denoising and Inpainting of Sonar Images Using Convolutional Sparse Representation

Recently, sparse representation (SR) techniques have been extensively applied for sound navigation and ranging (sonar) images’ restoration tasks such as denoising and inpainting. However, fine details such as edges and texture information present in sonar images are not fully restored using these techniques. This is due to ineffective dictionary formation and learning of sparse components and dictionaries. In this article, the author proposes the convolutional SR (CSR)-based methods for sonar image denoising and inpainting tasks. To minimize the Gaussian noise from sonar images, an alternative direction method of the multiplier (ADMM) optimization algorithm is used for solving the convolutional basis pursuit denoising (CBPDN) problem with joint sparsity through an
$L_{2,1}$
-norm term. For the removal of impulse noise from sonar images, an ADMM algorithm is used to solve a CSR problem with an
$L_{1}$
data fidelity term and both
$L_{1}$
and
$L_{2}$
gradient regularization terms. For the inpainting of sonar images, the additive mask simulation (MS) technique is used for solving CSR problems related to boundary masking. From the experimental results, it is found that the proposed sonar image denoising and inpainting methods have created better visual quality sonar images, higher peak signal-to-noise ratio (PSNR), and structure similarity (SSIM) values, when compared with the state-of-the-art sonar image denoising and inpainting methods.