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The unrolling method has been investigated for learning variational models in X-ray computed tomography. However, it has been observed that directly unrolling the regularization model through gradient descent does not produce satisfactory results. In this paper, we present a novel deep learning-based CT reconstruction model, where the low-resolution image is introduced to obtain an effective regularization term for improving the network`s robustness. Our approach involves constructing the backbone network architecture by algorithm unrolling that is realized using the deep equilibrium architecture. We theoretically discuss the convergence of the proposed low-resolution prior equilibrium model and provide the conditions to guarantee convergence. Experimental results on both sparse-view and limited-angle reconstruction problems are provided, demonstrating that our end-to-end low-resolution prior equilibrium model outperforms other state-of-the-art methods in terms of noise reduction, contrast-to-noise ratio, and preservation of edge details.

The convolutional neural network-based methods have become more and more popular for medical image segmentation due to their outstanding performance. However, they struggle with capturing long-range dependencies, which are essential for accurately modeling global contextual correlations. Thanks to the ability to model long-range dependencies by expanding the receptive field, the transformer-based methods have gained prominence. Inspired by this, we propose an advanced 2D feature extraction method by combining the convolutional neural network and Transformer architectures. More specifically, we introduce a parallelized encoder structure, where one branch uses ResNet to extract local information from images, while the other branch uses Transformer to extract global information. Furthermore, we integrate pyramid structures into the Transformer to extract global information at varying resolutions, especially in intensive prediction tasks. To efficiently utilize the different information in the parallelized encoder at the decoder stage, we use a channel attention module to merge the features of the encoder and propagate them through skip connections and bottlenecks. Intensive numerical experiments are performed on both aortic vessel tree, cardiac, and multi-organ datasets. By comparing with state-of-the-art medical image segmentation methods, our method is shown with better segmentation accuracy, especially on small organs. The code is publicly available on https://github.com/HongkunSun/ParaTransCNN.

Skin diseases are among the most prevalent health issues, and accurate computer-aided diagnosis methods are of importance for both dermatologists and patients. However, most of the existing methods overlook the essential domain knowledge required for skin disease diagnosis. A novel multi-task model, namely DermImitFormer, is proposed to fill this gap by imitating dermatologists' diagnostic procedures and strategies. Through multi-task learning, the model simultaneously predicts body parts and lesion attributes in addition to the disease itself, enhancing diagnosis accuracy and improving diagnosis interpretability. The designed lesion selection module mimics dermatologists' zoom-in action, effectively highlighting the local lesion features from noisy backgrounds. Additionally, the presented cross-interaction module explicitly models the complicated diagnostic reasoning between body parts, lesion attributes, and diseases. To provide a more robust evaluation of the proposed method, a large-scale clinical image dataset of skin diseases with significantly more cases than existing datasets has been established. Extensive experiments on three different datasets consistently demonstrate the state-of-the-art recognition performance of the proposed approach., Comment: MICCAI 2023 early accept

The challenges in recovering underwater images are the presence of diverse degradation factors and the lack of ground truth images. Although synthetic underwater image pairs can be used to overcome the problem of inadequately observing data, it may result in over-fitting and enhancement degradation. This paper proposes a model-based deep learning method for restoring clean images under various underwater scenarios, which exhibits good interpretability and generalization ability. More specifically, we build up a multi-variable convolutional neural network model to estimate the clean image, background light and transmission map, respectively. An efficient loss function is also designed to closely integrate the variables based on the underwater image model. The meta-learning strategy is used to obtain a pre-trained model on the synthetic underwater dataset, which contains different types of degradation to cover the various underwater environments. The pre-trained model is then fine-tuned on real underwater datasets to obtain a reliable underwater image enhancement model, called MetaUE. Numerical experiments demonstrate that the pre-trained model has good generalization ability, allowing it to remove the color degradation for various underwater attenuation images such as blue, green and yellow, etc. The fine-tuning makes the model able to adapt to different underwater datasets, the enhancement results of which outperform the state-of-the-art underwater image restoration methods. All our codes and data are available at \url{https://github.com/Duanlab123/MetaUE}.

Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight, which uses photon time-of-flight information encoded in light after multiple diffuse reflections. The under-sampled scanning data can facilitate fast imaging. However, the resulting reconstruction problem becomes a serious ill-posed inverse problem, the solution of which is highly possibility to be degraded due to noises and distortions. In this paper, we propose novel NLOS reconstruction models based on curvature regularization, i.e., the object-domain curvature regularization model and the dual (signal and object)-domain curvature regularization model. In what follows, we develop efficient optimization algorithms relying on the alternating direction method of multipliers (ADMM) with the backtracking stepsize rule, for which all solvers can be implemented on GPUs. We evaluate the proposed algorithms on both synthetic and real datasets, which achieve state-of-the-art performance, especially in the compressed sensing setting. Based on GPU computing, our algorithm is the most effective among iterative methods, balancing reconstruction quality and computational time. All our codes and data are available at https://github.com/Duanlab123/CurvNLOS.

Due to the development of deep learning-based denoisers, the plug-and-play strategy has achieved great success in image restoration problems. However, existing plug-and-play image restoration methods are designed for non-blind Gaussian denoising such as zhang et al (2022), the performance of which visibly deteriorate for unknown noises. To push the limits of plug-and-play image restoration, we propose a novel framework with blind Gaussian prior, which can deal with more complicated image restoration problems in the real world. More specifically, we build up a new image restoration model by regarding the noise level as a variable, which is implemented by a two-stage blind Gaussian denoiser consisting of a noise estimation subnetwork and a denoising subnetwork, where the noise estimation subnetwork provides the noise level to the denoising subnetwork for blind noise removal. We also introduce the curvature map into the encoder-decoder architecture and the supervised attention module to achieve a highly flexible and effective convolutional neural network. The experimental results on image denoising, deblurring and single-image super-resolution are provided to demonstrate the advantages of our deep curvature denoiser and the resulting plug-and-play blind image restoration method over the state-of-the-art model-based and learning-based methods. Our model is shown to be able to recover the fine image details and tiny structures even when the noise level is unknown for different image restoration tasks. The source codes are available at https://github.com/Duanlab123/CurvPnP.

In the practical applications of computed tomography imaging, the projection data may be acquired within a limited-angle range and corrupted by noises due to the limitation of scanning conditions. The noisy incomplete projection data results in the ill-posedness of the inverse problems. In this work, we theoretically verify that the low-resolution reconstruction problem has better numerical stability than the high-resolution problem. In what follows, a novel low-resolution image prior based CT reconstruction model is proposed to make use of the low-resolution image to improve the reconstruction quality. More specifically, we build up a low-resolution reconstruction problem on the down-sampled projection data, and use the reconstructed low-resolution image as prior knowledge for the original limited-angle CT problem. We solve the constrained minimization problem by the alternating direction method with all subproblems approximated by the convolutional neural networks. Numerical experiments demonstrate that our double-resolution network outperforms both the variational method and popular learning-based reconstruction methods on noisy limited-angle reconstruction problems.

The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners, and contrast. However, the dilemma between restoration quality and computational efficiency is an essential roadblock for high-order methods. In this paper, we propose fast multi-grid algorithms for minimizing both mean curvature and Gaussian curvature energy functionals without sacrificing accuracy for efficiency. Unlike the existing approaches based on operator splitting and the Augmented Lagrangian method (ALM), no artificial parameters are introduced in our formulation, which guarantees the robustness of the proposed algorithm. Meanwhile, we adopt the domain decomposition method to promote parallel computing and use the fine-to-coarse structure to accelerate convergence. Numerical experiments are presented on image denoising, CT, and MRI reconstruction problems to demonstrate the superiority of our method in preserving geometric structures and fine details. The proposed method is also shown effective in dealing with large-scale image processing problems by recovering an image of size $1024\times 1024$ within $40$s, while the ALM method requires around $200$s.

In this paper, we propose a new variational model for image reconstruction by minimizing the $L^1$ norm of the \emph{Weingarten map} of image surface $(x,y,f(x,y))$ for a given image $f:{\mathrm{\Omega}}\rightarrow \mathbb R$. We analytically prove that the Weingarten map minimization model can not only keep the greyscale intensity contrasts of images, but also preserve edges and corners of objects. The alternating direction method of multiplier (ADMM) based algorithm is developed, where one subproblem needs to be solved by gradient descent. In what follows, we derive a hybrid nonlinear first and second order regularization from the Weingarten map, and present an efficient ADMM-based algorithm by regarding the nonlinear weights as known. By comparing with several state-of-the-art methods on synthetic and real image reconstruction problems, it confirms that the proposed models can well preserve image contrasts and features, especially the spatially adapted first and second order regularization economizing much computational cost.

The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex, non-smooth and highly non-linear, the first-order optimal condition of which are high-order partial differential equations. Thus, the numerical computation are extremely challenging. In this paper, we propose to estimate the discrete curvatures, i.e., mean curvature and Gaussian curvature, in the local neighborhood according to differential geometry theory. By minimizing certain functions of curvatures on all level curves of an image, it yields a kind of weighted total variation minimization problem, which can be efficiently solved by the proximal alternating direction method of multipliers (ADMM). Numerical experiments are implemented to demonstrate the effectiveness and superiority of our proposed variational models for different image reconstruction tasks.

In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [4] in order to remove mixed Poisson-Gaussian(MPG) noise. In the existing splitting algorithm for TV-IC, an inner loop by Newton method had to be adopted for one nonlinear optimization subproblem, which increased the computation cost per outer loop. By introducing a new bilinear constraint and applying the alternating direction method of multipliers (ADMM), all subproblems of the proposed algorithms named as BCA (short for Bilinear Constraint based ADMM algorithm) and BCAf(short for a variant of BCA with fully splitting form) can be very efficiently solved; especially for the proposed BCAf, they can be calculated without any inner iterations. Under mild conditions, the convergence of the proposed BCA is investigated. Numerically, compared to existing primal-dual algorithms for the TV-IC model, the proposed algorithms, with fewer tunable parameters, converge much faster and produce comparable results meanwhile.