Multiplicative Noise and Blur Removal by Framelet Decomposition and -Based L-Curve Method

A Simplified Convex Optimization Model for Image Restoration with Multiplicative Noise

In this paper, we propose a novel convex variational model for image restoration with multiplicative noise. To preserve the edges in the restored image, our model incorporates a total variation regularizer. Additionally, we impose an equality constraint on the data fidelity term, which simplifies the model selection process and promotes sparsity in the solution. We adopt the alternating direction method of multipliers (ADMM) method to solve the model efficiently. To validate the effectiveness of our model, we conduct numerical experiments on both real and synthetic noise images, and compare its performance with existing methods. The experimental results demonstrate the superiority of our model in terms of PSNR and visual quality.

Synthetic Aperture Radar Image Despeckling Based on Multi-Weighted Sparse Coding

Synthetic aperture radar (SAR) images are inherently degraded by speckle noise caused by coherent imaging, which may affect the performance of the subsequent image analysis task. To resolve this problem, this article proposes an integrated SAR image despeckling model based on dictionary learning and multi-weighted sparse coding. First, the dictionary is trained by groups composed of similar image patches, which have the same structural features. An effective orthogonal dictionary with high sparse representation ability is realized by introducing a properly tight frame. Furthermore, the data-fidelity term and regularization terms are constrained by weighting factors. The weighted sparse representation model not only fully utilizes the interblock relevance but also reflects the importance of various structural groups in despeckling processing. The proposed model is implemented with fast and effective solving steps that simultaneously perform orthogonal dictionary learning, weight parameter updating, sparse coding, and image reconstruction. The solving steps are designed using the alternative minimization method. Finally, the speckles are further suppressed by iterative regularization methods. In a comparison study with existing methods, our method demonstrated state-of-the-art performance in suppressing speckle noise and protecting the image texture details.

Complex Wavelet-Based Image Watermarking with the Human Visual Saliency Model

Imperceptibility and robustness are the two complementary, but fundamental requirements of any digital image watermarking method. To improve the invisibility and robustness of multiplicative image watermarking, a complex wavelet based watermarking algorithm is proposed by using the human visual texture masking and visual saliency model. First, image blocks with high entropy are selected as the watermark embedding space to achieve imperceptibility. Then, an adaptive multiplicative watermark embedding strength factor is designed by utilizing texture masking and visual saliency to enhance robustness. Furthermore, the complex wavelet coefficients of the low frequency sub-band are modeled by a Gaussian distribution, and a watermark decoding method is proposed based on the maximum likelihood criterion. Finally, the effectiveness of the watermarking is validated by using the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM) through experiments. Simulation results demonstrate the invisibility of the proposed method and its strong robustness against various attacks, including additive noise, image filtering, JPEG compression, amplitude scaling, rotation attack, and combinational attack.