In this paper, we propose an ℓ0-based nonconvex optimization model with overlapping group sparse hyper-Laplacian prior (ℓ0-OGSHL) to remove stripes from remote sensing images (RSIs) effectively. Specifically, we utilize the hyper-Laplacian prior with overlapping group sparsity (OGSHL) to characterize the properties of the underlying image. Additionally, the related ℓ0-quasi equivalent is transformed into an easily solvable form by employing a mathematical program with equilibrium constraints (MPEC). Furthermore, the alternating direction method of multipliers (ADMM) algorithm is employed for resolving the equivalent nonconvex optimization model, and the complex OGSHL subproblem is addressed through the majorization-minimization (MM) method. Finally, the experimental results on the simulated datasets conclusively demonstrate the superior performance of the proposed method over the compared methods (with 1 3dB higher MPSNR), both quantitatively and visually. The code will be available after possible acceptance.

Non-blind deblurring methods achieve decent performance under the accurate blur kernel assumption. Since the kernel uncertainty (i.e. kernel error) is inevitable in practice, semi-blind deblurring is suggested to handle it by introducing the prior of the kernel (or induced) error. However, how to design a suitable prior for the kernel (or induced) error remains challenging. Hand-crafted prior, incorporating domain knowledge, generally performs well but may lead to poor performance when kernel (or induced) error is complex. Data-driven prior, which excessively depends on the diversity and abundance of training data, is vulnerable to out-of-distribution blurs and images. To address this challenge, we suggest a dataset-free deep residual prior for the kernel induced error (termed as residual) expressed by a customized untrained deep neural network, which allows us to flexibly adapt to different blurs and images in real scenarios. By organically integrating the respective strengths of deep priors and hand-crafted priors, we propose an unsupervised semi-blind deblurring model which recovers the clear image from the blurry image and inaccurate blur kernel. To tackle the formulated model, an efficient alternating minimization algorithm is developed. Extensive experiments demonstrate the favorable performance of the proposed method as compared to model-driven and data-driven methods in terms of image quality and the robustness to different types of kernel error.

Scene recovery is a fundamental imaging task with several practical applications, including video surveillance and autonomous vehicles, etc. In this article, we provide a new real-time scene recovery framework to restore degraded images under different weather/imaging conditions, such as underwater, sand dust and haze. A degraded image can actually be seen as a superimposition of a clear image with the same color imaging environment (underwater, sand or haze, etc.). Mathematically, we can introduce a rank-one matrix to characterize this phenomenon, i.e., rank-one prior (ROP). Using the prior, a direct method with the complexity$O(N)$is derived for real-time recovery. For general cases, we develop ROP$^+$to further improve the recovery performance. Comprehensive experiments of the scene recovery illustrate that our method outperforms competitively several state-of-the-art imaging methods in terms of efficiency and robustness.

Scene recovery is a fundamental imaging task for several practical applications, e.g., video surveillance and autonomous vehicles, etc. To improve visual quality under different weather/imaging conditions, we propose a real-time light correction method to recover the degraded scenes in the cases of sandstorms, underwater, and haze. The heart of our work is that we propose an intensity projection strategy to estimate the transmission. This strategy is motivated by a straightforward rank-one transmission prior. The complexity of transmission estimation is O(N ) where N is the size of the single image. Then we can recover the scene in real-time. Comprehensive experiments on different types of weather/imaging conditions illustrate that our method outperforms competitively several state-of-the-art imaging methods in terms of efficiency and robustness.

Blind image deblurring is a conundrum because there are infinitely many pairs of latent image and blur kernel. To get a stable and reasonable deblurred image, proper prior knowledge of the latent image and the blur kernel is urgently required. Different from the recent works on the statistical observations of the difference between the blurred image and the clean one, our method is built on the surface-aware strategy arising from the intrinsic geometrical consideration. This approach facilitates the blur kernel estimation due to the preserved sharp edges in the intermediate latent image. Extensive experiments demonstrate that our method outperforms the state-of-the-art methods on deblurring the text and natural images. Moreover, our method can achieve attractive results in some challenging cases, such as low-illumination images with large saturated regions and impulse noise. A direct extension of our method to the non-uniform deblurring problem also validates the effectiveness of the surface-aware prior.

Wavelet tight frames have been actively investigated for various image restoration problems. In this paper, we introduce an analysis-sparsity model via$\ell _2$-relaxed truncated$\ell _0$regularization and nonlocal estimation, and the resulted nonconvex minimization problem is tackled by a proximal alternating minimization strategy. Numerical experiments demonstrate that the proposed algorithm is superior to many popular methods in both objective and perceptual quality.

Image smoothing is a very important topic in image processing. Among these image smoothing methods, the L0gradient minimization method is one of the most popular ones. However, the L0gradient minimization method suffers from the staircasing effect and over-sharpening issue, which highly degrade the quality of the smoothed image. To overcome these issues, we use not only the L0gradient term for finding edges, but also a surface area based term for the purpose of smoothing the inside of each region. An alternating minimization algorithm is suggested to efficiently solve the proposed model, where each subproblem has a closed-form solution. Leveraging the introduced surface area term, the proposed method can effectively alleviate the staircasing effect and the over-sharpening issue. The superiority of our method over the state-of-the-art methods is demonstrated by a series of experiments.