The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color artifacts in deblurring process. To solve this challenging problem, we present a novel cross-space total variation (CSTV) regularization model for color image deblurring by introducing a quaternion blur operator and a cross-color space regularization functional. The existence and uniqueness of the solution is proved and a new L-curve method is proposed to find a balance of regularization terms on different color spaces. The Euler-Lagrange equation is derived to show that CSTV has taken into account the coupling of all color channels and the local smoothing within each color channel. A quaternion operator splitting method is firstly proposed to enhance the ability of color artifacts reduction of the CSTV regularization model. This strategy also applies to the well-known color deblurring models. Numerical experiments on color image databases illustrate the efficiency and effectiveness of the new model and algorithms. The color images restored by them successfully maintain the color and spatial information and are of higher quality in terms of PSNR, SSIM, MSE and CIEde2000 than the restorations of the-state-of-the-art methods.

Incremental Object Detection (IOD) simulates the dynamic data flow in real-world applications, which require detectors to learn new classes or adapt to new domains while retaining knowledge from previous tasks. Most existing IOD methods focus only on class incremental learning, assuming all data comes from the same domain. However, this is hardly achievable in practical applications, as images collected under different conditions often exhibit completely different characteristics, such as lighting, weather, style, etc. Class IOD methods suffer from performance degradation in these scenarios with domain shifts. To bridge domain shifts and category gaps in IOD, we propose Purified Distillation (PD), where we use a set of trainable queries to transfer the teacher's attention on old tasks to the student and adopt the gradient reversal layer to guide the student to learn the teacher's feature space structure from a micro perspective, which has not been extensively studied in previous works. Meanwhile, PD combines classification confidence with localization confidence to purify the most meaningful output nodes, so that the student model inherits a more comprehensive teacher knowledge. Extensive experiments across various IOD settings on six widely used datasets show that PD significantly outperforms state-of-the-art methods. Even after five steps of incremental learning, our method can preserve 60.6% mAP on the first task, while compared methods can only maintain up to 55.9%.

The Retinex model is one of the most representative and effective methods for low-light image enhancement. However, the Retinex model does not explicitly tackle the noise problem and shows unsatisfactory enhancing results. In recent years, due to the excellent performance, deep learning models have been widely used in low-light image enhancement. However, these methods have two limitations. First, the desirable performance can only be achieved by deep learning when a large number of labeled data are available. However, it is not easy to curate massive low-/normal-light paired data. Second, deep learning is notoriously a black-box model. It is difficult to explain their inner working mechanism and understand their behaviors. In this article, using a sequential Retinex decomposition strategy, we design a plug-and-play framework based on the Retinex theory for simultaneous image enhancement and noise removal. Meanwhile, we develop a convolutional neural network-based (CNN-based) denoiser into our proposed plug-and-play framework to generate a reflectance component. The final image is enhanced by integrating the illumination and reflectance with gamma correction. The proposed plug-and-play framework can facilitate both post hoc and ad hoc interpretability. Extensive experiments on different datasets demonstrate that our framework outcompetes the state-of-the-art methods in both image enhancement and denoising.

Single-particle reconstruction (SPR) in cryogenic electron microscopy (cryo-EM) aims at aligning and averaging two-dimensional micrographs to reconstruct a three-dimensional particle. How to reconstruct micrographs from heavy noise is a crucial point for achieving better micrograph quality, and thus many methods focus on noise removal. However, new problems such as over-smoothing often occur in their results due to failure in handling heavy noise well. This paper proposes a three-dimensional weighted nuclear norm minimization (3DWNNM) model for SPR in the cryo-EM task to address these issues. Specifically, we design a minimization solver based on the forward-backward splitting algorithm to tackle our model efficiently. Under certain conditions, this solution has an energy-decaying feature and performs exceptionally well in reconstruction. Numerical experiments fully demonstrate the effectiveness and the robustness of the proposed method.

Image deblurring under Rician noise has attracted considerable attention in imaging science. Frequently appearing in medical imaging, Rician noise leads to an interesting nonconvex optimization problem, termed as the MAP-Rician model, which is based on the Maximum a Posteriori (MAP) estimation approach. As the MAP-Rician model is deeply rooted in Bayesian analysis, we want to understand its mathematical analysis carefully. Moreover, one needs to properly select a suitable algorithm for tackling this nonconvex problem to get the best performance. This paper investigates both issues. Indeed, we first present a theoretical result about the existence of a minimizer for the MAP-Rician model under mild conditions. Next, we aim to adopt an efficient boosted difference of convex functions algorithm (BDCA) to handle this challenging problem. Basically, BDCA combines the classical difference of convex functions algorithm (DCA) with a backtracking line search, which utilizes the point generated by DCA to define a search direction. In particular, we apply a smoothing scheme to handle the nonsmooth total variation (TV) regularization term in the discrete MAP-Rician model. Theoretically, using the Kurdyka--Lojasiewicz (KL) property, the convergence of the numerical algorithm can be guaranteed. We also prove that the sequence generated by the proposed algorithm converges to a stationary point with the objective function values decreasing monotonically. Numerical simulations are then reported to clearly illustrate that our BDCA approach outperforms some state-of-the-art methods for both medical and natural images in terms of image recovery capability and CPU-time cost.

Image enhancement is a technique to enhance the illumination of dark images while keeping the reality and the naturalness of the enhanced images at the same time. For color images, most methods tackle different color channels in a separate way, which overlooks the connection between the color channels. Therefore, in this paper, we consider a quaternion-based model to reserve the color connectivity, which integrates the color information of a pixel by a quaternion number. Moreover, we propose a regularizer based on the gamma-correction function and incorporate it into a screened Poisson equation for the image enhancement task. The uniqueness and existence of the solution of the proposed model are analyzed. The numerical results also prove the superiority of our scheme for color image enhancement.

Color image restoration is a critical task in imaging sciences. Most variational methods regard the color image as a Euclidean vector or the direct combination of three monochrome images and completely ignore the inherent color structures within channels. To better describe the relationship of color channels, we represent the color image as the so-called pure quaternion matrix. Note that the celebrated dictionary learning method has attracted considerable attention for image recovery in the past decade. Following this idea, we propose a novel quaternion-based color image recovery method. This model combines the advantages of dictionary learning and the total variation method for color image restoration. The new strategy used in the proposed model manages to handle the color image restoration problem in the quaternion space. Moreover, the new proposed model can be easily solved by the classical alternating direction method of multipliers (ADMM) algorithm. Numerical results demonstrate clearly that the performance of our proposed dictionary learning method is better than some state-of-the-art color image dictionary learning and total variation methods in terms of some criteria and visual quality.

Abstract Image segmentation is a fundamental and challenging task in image processing and computer vision. The colour image segmentation is attracting more attention as the colour image provides more information than the grey image. A variational model based on a convex K‐means approach to segment colour images is proposed. The proposed variational method uses a combination of l 1 and l 2 regularizers to maintain edge information of objects in images while overcoming the staircase effect. Meanwhile, our one‐stage strategy is an improved version based on the smoothing and thresholding strategy, which contributes to improving the accuracy of segmentation. The proposed method performs the following steps. First, the colour set which can be determined by human or the K‐means method is specified. Second, a variational model to obtain the most appropriate colour for each pixel from the colour set via convex relaxation and lifting is used. The Chambolle–Pock algorithm and simplex projection are applied to solve the variational model effectively. Experimental results and comparison analysis demonstrate the effectiveness and robustness of the method.

Cauchy noise, as a typical non-Gaussian noise, appears frequently in many important fields, such as radar, medical, and biomedical imaging. In this letter, we focus on image recovery under Cauchy noise. Instead of the celebrated total variation or low-rank prior, we adopt a novel deep-learning-based image denoiser prior to effectively remove Cauchy noise with blur. To preserve more detailed texture and better balance between the receptive field size and the computational cost, we apply the multi-level wavelet convolutional neural network (MWCNN) to train this denoiser. We use the forward-backward splitting (FBS) method to handle the proposed model, which can be implemented efficiently without introducing auxiliary variables. Moreover, the multi-noise-levels strategy is employed to train a series of denoisers to restore the image corrupted by Cauchy noise and blur. Numerical experiments demonstrate clearly that our method has better performance than the existing image restoration methods for removing Cauchy noise in terms of the quantitative index and visual quality.