Wavelet frame-based image restoration using sparsity, nonlocal, and support prior of frame coefficients

Abstract

The wavelet frame systems have been widely investigated and applied for image restoration and many other image processing problems over the past decades, attributing to their good capability of sparsely approximating piece-wise smooth functions such as images. Most wavelet frame based models exploit the l 1 norm of frame coefficients for a sparsity constraint in the past. The authors in [50,17] proposed an l 0 minimization model, where the l 0 norm of wavelet frame coefficients is penalized instead, and have demonstrated that significant improvements can be achieved compared to the commonly used l 1 minimization model. Very recently, the authors in [11] proposed l 0 -l 2 minimization model, where the nonlocal prior of frame coefficients is incorporated. This model proved to outperform the single l 0 minimization based model in terms of better recovered image quality. In this paper, we propose a truncated l 0 -l 2 minimization model which combines sparsity, nonlocal and support prior of the frame coefficients. The extensive experiments have shown that the recovery results from the proposed regularization method performs better than existing state-of-the-art wavelet frame based methods, in terms of edge enhancement and texture preserving performance.

Spatial Signal Detection Using Continuous Shrinkage Priors

“…The two-dimensional fused lasso (Friedman et al, 2007) and the graphical lasso (Friedman et al, 2008) are penalized regression methods that account for spatial structure in the signal using penalties to encourage spatial smoothness. Spatial wavelet shrinkage methods impose a threshold on coefficients in the wavelet domain to recover a sparse signal (Donoho and Johnstone, 1994;Taswell, 2000;Jansen, 2001;Yadav et al, 2014;He and Xiang, 2017). These regularization methods can be applied to high-dimensional data, but require presetting the tuning parameters via cross validation (Mallick and Yi, 2013) and fail to account for all sources of uncertainty.…”

Adaptive wavelet tight frame construction for accelerating MRI reconstruction

“…However, due to the nonconvex objective function in (8), the convergence of iterates in the algorithm cannot be theoretically guaranteed. To yield a convergence result, several strategies have been adopted such as replacing the ℓ 0 pseudo-norm by ℓ 1 norm [28,29,30], and gradually decreasing the regularization parameters during iterations [13], etc.…”

Face Image Publication Based on Differential Privacy

“…References [20][21][22][23] propose using pixel replacement or pixel value substitution to encrypt image content. References [24][25][26][27][28] encrypt the image by changing the transform coefficient of the image in the frequency domain. Similar to the problems of anonymization technology, data encryption technology will also make corresponding assumptions for attacks and then design the corresponding encryption algorithm based on these assumptions.…”