Underwater Acoustic Image Denoising Using Stationary Wavelet Transform and Various Shrinkage Functions

Underwater acoustic images are captured by sonar technology which uses sound as a source. The noise in the acoustic images may occur only during acquisition. These noises may be multiplicative in nature and cause serious effects on the images affecting their visual quality. Generally image denoising techniques that remove the noise from the images can use linear and non-linear filters. In this paper, wavelet based denoising method is used to reduce the noise from the images. The image is decomposed using Stationary Wavelet Transform (SWT) into low and high frequency components. The various shrinkage functions such as Visushrink and Sureshrink are used for selecting the threshold to remove the undesirable signals in the low frequency component. The high frequency components such as edges and corners are retained. Then the inverse SWT is used for reconstruction of denoised image by combining the modified low frequency components with the high frequency components. The performance measure Peak Signal to Noise Ratio (PSNR) is obtained for various wavelets such as Haar, Daubechies,Coiflet and by changing the thresholding methods.

Analytical and Simple Form of Shrinkage Functions for Non-Convex Penalty Functions in Fused Lasso Algorithm

In some circumstances, the performance of machine learning (ML) tasks are based on the quality of signal (data) that is processed in these tasks. Therefore, the pre-processing techniques, such as reconstruction and denoising methods, are important techniques in ML tasks. In reconstructed (estimated) method, the fused lasso algorithm with non-convex penalty function is an efficient method when the signal corrupted by additive white Gaussian noise (AWGN) is considered. Therefore, this paper proposes new shrinkage functions for non-convex penalty functions, modified arctangent and exponential models, in fused lasso formulation. A lot of works present the shrinkage function for arctangent penalty function. Unfortunately, there is no closed-form solution. The numerical solution is required for shrinkage function of this penalty function. However, the analytical solution is derived in this paper. Moreover, the shrinkage function of modified exponential penalty function is proposed. This shrinkage function obtains from simple iterative method, fixed-point algorithm. We demonstrate the proposed methods through simulations with standard one-dimensional signals contaminated by AWGN. The proposed techniques are compared with traditional estimation methods, such as total variation (TV) and wavelet denoising methods. In experimental results, our proposed methods outperform several exiting methods both visual quality and in terms of root mean square error (RMSE). In fact, the proposed methods can better preserve the feature of noise-free signal than the compared methods. The denoised signals produced by the proposed methods are less smooth than the denoised signals produced by the compared methods.

A MULTISCALE TIGHT FRAME-INSPIRED SCHEME FOR NONLINEAR DIFFUSION

Nonlinear diffusion and wavelet shrinkage are two successfully applied methods for discontinuity preserving denoising of signals and images. Recently, relations between both methods have been established taking into account wavelet shrinkage at one or multiscale. In this paper we show that one step of (stabilized) explicit discretization of nonlinear diffusion can be expressed in terms of tight frame shrinkage on a single spatial level or multiscale. We prove that our scheme permits larger steps while having more choices of shrinkage functions. Numerical examples demonstrate the behavior of our scheme for one or two scales.