DNA-based data storage offers an attractive alternative to traditional media due to its exceptional density, durability, and sustainability. However, errors introduced across the DNA storage pipeline critically impede accurate sequence reconstruction from noisy sequencing reads. This paper addresses the DNA sequence reconstruction problem by proposing FedDNA, a novel Personalized Federated Learning (PFL) framework based on Evidential Deep Learning (DEL), designed for DNA storage environments. FedDNA quantifies robust predictive uncertainty through a novel evidence fusion mechanism that aggregates evidence from each noisy read in a cluster, thereby enhancing client-level prediction reliability. For efficient sequence modeling and reconstruction from these noisy clusters, its architecture employs a convolution-enhanced Mamba encoder and an LSTM decoder. To address prohibitive centralized training costs, privacy concerns, and data heterogeneity across diverse DNA storage data, FedDNA integrates PFL and designs an innovative uncertainty-driven personalized aggregation strategy based on epistemic and aleatoric decomposition, for which we also provide rigorous theoretical generalization bounds. Experimental results demonstrate FedDNA achieves superior reconstruction performance on DNA storage data with heterogeneity, highlighting its potential for secure and efficient DNA storage systems.

Abstract. We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic properties. To tackle the resulting high-order nonlinear optimization problem, we reformulate it as the task of finding the steady-state solution of a time-dependent partial differential equation (PDE) system. Time discretization is achieved through operator splitting, where each subproblem at the fractional steps either has a closed-form solution or can be efficiently solved using advanced algorithms. Our method circumvents the need for complex parameter tuning and demonstrates robustness to parameter choices. The efficiency and effectiveness of our approach have been rigorously validated in the context of surface and image smoothing problems.

The elliptical shape prior information plays a vital role in improving the accuracy of image segmentation for specific tasks in medical and natural images. Existing deep learning-based segmentation methods, including the Segment Anything Model (SAM), often struggle to produce segmentation results with elliptical shapes efficiently. This paper proposes a new approach to integrate the prior of elliptical shapes into the deep learning-based SAM image segmentation techniques using variational methods. The proposed method establishes a parameterized elliptical contour field, which constrains the segmentation results to align with predefined elliptical contours. Utilizing the dual algorithm, the model seamlessly integrates image features with elliptical priors and spatial regularization priors, thereby greatly enhancing segmentation accuracy. By decomposing the SAM into four mathematical subproblems, we integrate the variational ellipse prior to design a new SAM network structure, ensuring that the segmentation output of the SAM consists of elliptical regions. Experimental results on some specific image datasets demonstrate an improvement over the original SAM. The codes are available in https://github.com/zhaoxinyum/SAM-ESP.

Normal reconstruction is crucial in non-line-of-sight (NLOS) imaging, as it provides key geometric and lighting information about hidden objects, which significantly improves reconstruction accuracy and scene understanding. However, jointly estimating normals and albedo expands the problem from matrix-valued functions to tensor-valued functions that substantially increasing complexity and computational difficulty. In this paper, we propose a novel joint albedo-surface reconstruction method, which utilizes the shape operator to control the variation rate of the normal field. It is the first attempt to apply regularization methods to the reconstruction of surface normals for hidden objects. By improving the accuracy of the normal field, it enhances detail representation and achieves high-precision reconstruction of hidden object geometry. The proposed method demonstrates robustness and effectiveness on both synthetic and experimental datasets. On transient data captured within 15 seconds, our surface normal-regularized reconstruction model produces more accurate surfaces than recently proposed methods and is 30 times faster than the existing surface reconstruction approach.

Medical image segmentation is vital for clinical applications, with hard samples playing a key role in segmentation accuracy. We propose an effective image segmentation framework that includes mechanisms for identifying and segmenting hard samples. It derives a novel image segmentation paradigm: 1) Learning to identify hard samples: automatically selecting inherent hard samples from different datasets, and 2) Learning to segment hard samples: achieving the segmentation of hard samples through effective feature augmentation on dedicated networks. We name our method ‘Learning to Segment hard samples’ (L2S). The hard sample identification module comprises a backbone model and a classifier, which dynamically uncovers inherent dataset patterns. The hard sample segmentation module utilizes the diffusion process for feature augmentation and incorporates a more sophisticated segmentation network to achieve precise segmentation. We justify our motivation through solid theoretical analysis and extensive experiments. Evaluations across various modalities show that our L2S outperforms other SOTA methods, particularly by substantially improving the segmentation accuracy of hard samples. On ISIC dataset, our L2S improves the Dice score on hard samples and overall segmentation by 8.97% and 1.01%, respectively, compared to SOTA methods. The code is available at https://github.com/TqlYuanGie/L2S.

Non-line-of-sight (NLOS) imaging is an ill-posed problem to reconstruct hidden 3D scenes by leveraging photon time-of-flight information from diffusely reflected light. In the existing regularization models, the spatial residuals were handled by a single distribution, failing to account for the distinct characteristics of background and target objects. In this paper, we propose a novel NLOS reconstruction method that models the non-Gaussian residuals with a mixture distribution. Through a dual method, we derive an adaptive weighted residual model, where the weights generated in the dual space act as a zero-shot attention mechanism to control the contributions of different regions. The corresponding optimization problem can be effectively solved using the alternating minimization algorithm. Numerical experiments on both synthetic and real-world datasets demonstrate that our method surpasses the related existing approaches, achieving state-of-the-art performance. The code is available at:https://github.com/qiuxuanzhizi/AMD-NLOS-V1.

DNA is a promising storage medium, offering advantages in high density, long durability, and low maintenance cost. However, information recovery in DNA storage systems is challenged by errors arising during synthesis, amplification, and sequencing phases. A key challenge in decoding is sequence reconstruction, which involves recovering the original reference sequence from a set of noisy copies. While recent research has explored deep learning-based methods for this task, the high cost of synthesis and sequencing results in a limited availability of training samples. To overcome this challenge, we propose TransDNA, a deep transfer learning network specifically designed for sequence reconstruction in DNA storage. It consists of an encoder, a domain-specific decoder, and a domain-invariant feature extractor, with alternating domain alignment and domain-specific reconstruction mechanisms. By transferring knowledge from a larger source dataset, TransDNA significantly enhances the reconstruction success rate on two target datasets from real DNA storage experiments, outperforming the base model without transfer learning and several comparative methods. Notably, TransDNA surpasses the SDG method in both reconstruction success rate and training efficiency. These results demonstrate the effectiveness of TransDNA as the first transfer learning approach applied to the DNA sequence reconstruction task.

Diagnosing malignant skin tumors accurately at an early stage can be challenging due to ambiguous and even confusing visual characteristics displayed by various categories of skin tumors. To improve diagnosis precision, all available clinical data from multiple sources, particularly clinical images, dermoscopy images, and medical history, could be considered. Aligning with clinical practice, we propose a novel Transformer model, named RemixFormer++ that consists of a clinical image branch, a dermoscopy image branch, and a metadata branch. Given the unique characteristics inherent in clinical and dermoscopy images, specialized attention strategies are adopted for each type. Clinical images are processed through a top-down architecture, capturing both localized lesion details and global contextual information. Conversely, dermoscopy images undergo a bottom-up processing with two-level hierarchical encoders, designed to pinpoint fine-grained structural and textural features. A dedicated metadata branch seamlessly integrates non-visual information by encoding relevant patient data. Fusing features from three branches substantially boosts disease classification accuracy. RemixFormer++ demonstrates exceptional performance on four single-modality datasets (PAD-UFES-20, ISIC 2017/2018/2019). Compared with the previous best method using a public multi-modal Derm7pt dataset, we achieved an absolute 5.3% increase in averaged F1 and 1.2% in accuracy for the classification of five skin tumors. Furthermore, using a large-scale in-house dataset of 10,351 patients with the twelve most common skin tumors, our method obtained an overall classification accuracy of 92.6%. These promising results, on par or better with the performance of 191 dermatologists through a comprehensive reader study, evidently imply the potential clinical usability of our method.

With the exponential growth of digital data, there is a pressing need for innovative storage media and techniques. DNA molecules, due to their stability, storage capacity, and density, offer a promising solution for information storage. However, DNA storage also faces numerous challenges, such as complex biochemical constraints and encoding efficiency. This paper presents Explorer, a high-efficiency DNA coding algorithm based on the De Bruijn graph, which leverages its capability to characterize local sequences. Explorer enables coding under various biochemical constraints, such as homopolymers, GC content, and undesired motifs. This paper also introduces Codeformer, a fast decoding algorithm based on the transformer architecture, to further enhance decoding efficiency. Numerical experiments indicate that, compared with other advanced algorithms, Explorer not only achieves stable encoding and decoding under various biochemical constraints but also increases the encoding efficiency and bit rate by ¿10%. Additionally, Codeformer demonstrates the ability to efficiently decode large quantities of DNA sequences. Under different parameter settings, its decoding efficiency exceeds that of traditional algorithms by more than two-fold. When Codeformer is combined with Reed-Solomon code, its decoding accuracy exceeds 99%, making it a good choice for high-speed decoding applications. These advancements are expected to contribute to the development of DNA-based data storage systems and the broader exploration of DNA as a novel information storage medium.

Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes by using time-of-flight photon information 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 likely 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.

The curvature regularization method is well-known for its good geometric interpretability and strong priors in the continuity of edges, which has been applied to various image processing tasks. However, due to the non-convex, non-smooth, and highly non-linear intrinsic limitations, most existing algorithms lack a convergence guarantee. This paper proposes an efficient yet accurate scalar auxiliary variable (SAV) scheme for solving both mean curvature and Gaussian curvature minimization problems. The SAV-based algorithms are shown unconditionally energy diminishing, fast convergent, and very easy to be implemented for different image applications. Numerical experiments on noise removal, image deblurring, and single image super-resolution are presented on both gray and color image datasets to demonstrate the robustness and efficiency of our method. Source codes are made publicly available athttps://github.com/Duanlab123/SAV-curvature.

The formation of underwater images is a complex physical process that often suffers from various degradation factors, such as blurriness, low contrast, and color casts, which pose challenges for underwater object detection and recognition tasks. Because of the absence of reference images, learning-based methods that rely on unpaired images have been employed to enhance the underwater images. However, these methods may lose their effectiveness in real-world complex underwater environments. In this paper, we propose a model-driven cycle-consistent generative adversarial network (CycleGAN) model, which is inspired by the underwater image formation model to estimate the background light, transmission map, scene depth, and attenuation coefficient directly. Comprehensive experiments have demonstrated that our approach surpasses the compared underwater image restoration methods in both qualitative and quantitative aspects, providing restored images with satisfactory color saturation and brightness. We also conduct experiments on underwater object detection to illustrate the effectiveness of our CycleGAN in improving the detection accuracy. All our source codes and data are available at https://github.com/Duanlab123/UW-CycleGAN.

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 40s, while the ALM-based method requires around 200s.

We propose a novel variational method for Rician noise removal in magnitude-based magnetic resonance (MR) imaging. We first explore the link between the Gaussian noise removal for complex images and the Rician noise removal for magnitude images. Then we establish the constraint optimization model via signal-noise splitting, consisting of a total variation regularizer, two quadratic terms, and a constraint on the field of spheres. Specifically, this constraint represents the forward model of calculating the magnitude of complex images corrupted by Gaussian noises. Namely, the proposed model is completely different from the existing maximum a posteriori based methods, which inevitably involved the sophisticated Bessel function causing high computation costs. It is further efficiently solved by the alternating direction method of multipliers with convergence guarantee. Numerical comparisons with existing variational methods show that the proposed method produces comparable results in terms of image quality, but saves about 50% of overall computational cost on average.

The curvature regularities have received growing attention with the advantage of providing strong priors in the continuity of edges in image processing applications. However, owing to the non-convex and non-smooth properties of the high-order regularizer, the numerical solution becomes challenging in real-time tasks. In this paper, we propose a novel curvature regularity, the total curvature (TC), by minimizing the normal curvatures along different directions. We estimate the normal curvatures discretely in the local neighborhood according to differential geometry theory. The resulting curvature regularity can be regarded as a re-weighted total variation (TV) minimization problem, which can be efficiently solved by the alternating direction method of multipliers (ADMM) based algorithm. By comparing with TV and Euler's elastica energy, we demonstrate the effectiveness and superiority of the total curvature regularity for various image processing applications.

Rician noise reduction is an essential issue in magnetic resonance imaging (MRI). Recently, learning‐based methods have achieved great success in dealing with image restoration problems, which provide fast inference and good performance. One limitation of these methods, however, is that the training procedure is usually noise‐level dependent, i.e. the trained models are bound to a specific noise level and lack the ability to automatically adapt to different noise levels. In this study, the authors propose a variational model for Rician noise removal by integrating a noise adaption function into the field of experts image prior, which can adapt to different noise levels. Instead of directly solving the energy minimisation problem, the authors unroll the gradient descent step of the energy functional for several iterations, the time‐dependent parameters of which can be learned through a supervised training process. The authors call this methodology as the noise adaptive trainable non‐linear reaction–diffusion model. The proposed methodology is robustness against noise level changing and noise distributions. Experimental results over ‐, ‐ and PD‐weighted MRI data set demonstrate that the proposed model can achieve superior performance compared with other methods in terms of both the peak signal‐to‐noise ratio and the structural similarity index.

The Mumford-Shah model is an important tool for image labeling and segmentation, which pursues a piecewise smooth approximation of the original image and the boundaries with the shortest length. In contrast to previous efforts, which use the total variation regularization to measure the total length of the boundaries, we build up a novel piecewise smooth Mumford-Shah model by utilizing a non-convex ℓpregularity term for p ∈ (0,1), which can well preserve sharp edges and eliminate geometric staircasing effects. We present optimization algorithms with convergence verification, where all subproblems can be solved by either the closed-form solution or fast Fourier transform (FFT). The method is compared to piecewise constant labeling algorithm and several state-of-the-art piecewise smooth Mumford-Shah models based on image decomposition approximations. Both labeling and segmentation results on synthetic and real images confirm the robustness and efficiency of the proposed method.

Exploiting sparsity in the image gradient magnitude has proved effective in preserving sharp edges and reducing noises for many image processing tasks. Based on observation, we build up a novel piecewise smooth segmentation model by utilizing a generalized total variation (TV) prior with p-th power for and a l1data fidelity. We present an efficient algorithm based on the alternating direction method of multipliers (ADMM), where all subproblems can be solved by either one-step Gauss-Seidel iteration or the closed-form solution. Numerical experiments show that the proposed model can achieve more accurate segmentation results than the classical TV based segmentation model.

Phase retrieval plays an important role in vast industrial and scientific applications. We consider a noisy phase retrieval problem in which the magnitudes of the Fourier transform (or a general linear transform) of an underling object are corrupted by Poisson noise, since any optical sensors detect photons, and the number of detected photons follows the Poisson distribution. We propose a variational model for phase retrieval based on a total variation regularization as an image prior and maximum a posteriori estimation of a Poisson noise model, which is referred to as “TV-PoiPR”. We also propose an efficient numerical algorithm based on an alternating direction method of multipliers and establish its convergence. Extensive experiments for coded diffraction, holographic, and ptychographic patterns are conducted using both real- and complex-valued images to demonstrate the effectiveness of our proposed methods.

Retinex theory deals with compensation for illumination effects in images, which is usually an ill-posed problem. The existence of noises may severely challenge the performance of Retinex algorithms. Therefore, the main aim of this paper is to present a general variational Retinex model to effectively and robustly restore images corrupted by both noises and intensity inhomogeneities. Our strategy is to simultaneously recover the noise-free image and decompose it into reflectance and illumination component. The proposed model can be solved efficiently using the Alternating Direction Method of Multiplier (ADMM). Numerous experiments are conducted to demonstrate the advantages of the proposed model with Retinex illusions and medical image bias field correction for images in presence of Gaussian noise or impulsive noise.

In this paper, we focus on the "blind" identification of the computed tomography (CT) scanner that has produced a CT image. To do so, we propose a set of noise features derived from the image chain acquisition and which can be used as CT-scanner footprint. Basically, we propose two approaches. The first one aims at identifying a CT scanner based on an original sensor pattern noise (OSPN) that is intrinsic to the X-ray detectors. The second one identifies an acquisition system based on the way this noise is modified by its three-dimensional (3-D) image reconstruction algorithm. As these reconstruction algorithms are manufacturer dependent and kept secret, our features are used as input to train a support vector machine (SVM) based classifier to discriminate acquisition systems. Experiments conducted on images issued from 15 different CT-scanner models of 4 distinct manufacturers demonstrate that our system identifies the origin of one CT image with a detection rate of at least 94% and that it achieves better performance than sensor pattern noise (SPN) based strategy proposed for general public camera devices.

Brain extraction is an important preprocessing step for further analysis of brain MR images. Significant intensity inhomogeneity can be observed in rodent brain images due to the high-field MRI technique. Unlike most existing brain extraction methods that require bias corrected MRI, we present a high-order and L0regularized variational model for bias correction and brain extraction. The model is composed of a data fitting term, a piecewise constant regularization and a smooth regularization, which is constructed on a 3-D formulation for medical images with anisotropic voxel sizes. We propose an efficient multi-resolution algorithm for fast computation. At each resolution layer, we solve an alternating direction scheme, all subproblems of which have the closed-form solutions. The method is tested on three T2 weighted acquisition configurations comprising a total of 50 rodent brain volumes, which are with the acquisition field strengths of 4.7 Tesla, 9.4 Tesla and 17.6 Tesla, respectively. On one hand, we compare the results of bias correction with N3 and N4 in terms of the coefficient of variations on 20 different tissues of rodent brain. On the other hand, the results of brain extraction are compared against manually segmented gold standards, BET, BSE and 3-D PCNN based on a number of metrics. With the high accuracy and efficiency, our proposed method can facilitate automatic processing of large-scale brain studies.

An interactive surgical simulation system needs to meet three main requirements, speed, accuracy, and stability. In this paper, we present a stable and accurate method for animating mass-spring systems in real time. An integration scheme derived from explicit integration is used to obtain interactive realistic animation for a multiobject environment. We explore a predictor-corrector approach by correcting the estimation of the explicit integration in a poststep process. We introduce novel constraints on positions into the mass-spring model (MSM) to model the nonlinearity and preserve volume for the realistic simulation of the incompressibility. We verify the proposed MSM by comparing its deformations with the reference deformations of the nonlinear finite-element method. Moreover, experiments on porcine organs are designed for the evaluation of the multiobject deformation. Using a pair of freshly harvested porcine liver and gallbladder, the real organ deformations are acquired by computed tomography and used as the reference ground truth. Compared to the porcine model, our model achieves a 1.502 mm mean absolute error measured at landmark locations for cases with small deformation (the largest deformation is 49.109 mm) and a 3.639 mm mean absolute error for cases with large deformation (the largest deformation is 83.137 mm). The changes of volume for the two deformations are limited to 0.030% and 0.057%, respectively. Finally, an implementation in a virtual reality environment for laparoscopic cholecystectomy demonstrates that our model is capable to simulate large deformation and preserve volume in real-time calculations.

We propose a new variant of the Mumford-Shah model for simultaneous bias correction and segmentation of images with intensity inhomogeneity. First, based on the model of images with intensity inhomogeneity, we introduce an L0 gradient regularizer to model the true intensity and a smooth regularizer to model the bias field. In addition, we derive a new data fidelity using the local intensity properties to allow the bias field to be influenced by its neighborhood. Second, we use a two-stage segmentation method, where the fast alternating direction method is implemented in the first stage for the recovery of true intensity and bias field and a simple thresholding is used in the second stage for segmentation. Different from most of the existing methods for simultaneous bias correction and segmentation, we estimate the bias field and true intensity without fixing either the number of the regions or their values in advance. Our method has been validated on medical images of various modalities with intensity inhomogeneity. Compared with the state-of-art approaches and the well-known brain software tools, our model is fast, accurate, and robust with initializations.

This paper presents a novel discrete Mumford-Shah model for the simultaneous bias correction and image segmentation(SBCIS) for images with intensity inhomogeneity. The model is based on the assumption that an image can be approximated by a product of true intensities and a bias field. Unlike the existing methods, where the true intensities are represented as a linear combination of characteristic functions of segmentation regions, we employ L0gradient minimization to enforce a piecewise constant solution. We introduce a new neighbor term into the Mumford-Shah model to allow the true intensity of a pixel to be influenced by its immediate neighborhood. A two-stage segmentation method is applied to the proposed Mumford-Shah model. In the first stage, both the true intensities and bias field are obtained while the segmentation is done using the K-means clustering method in the second stage. Comparisons with the two-stage Mumford-Shah model show the advantages of our method in its ability in segmenting images with intensity inhomogeneity.

In this paper, we present the results of a preliminary work which focuses on identifying the system one Digital Radiography (DR) image has been produced by. To do so, we adapt one solution proposed for digital camera devices where the photo response non-uniformity noise of charge coupled device sensors is used as camera fingerprint. In particular, we show that DR acquisition systems leave a similar Digital Radiography Pattern Noise (DRPN) that can be used as fingerprint. In order to extract this DRPN and due to the nature of DR images, we further propose to take advantage of contourlet filtering. Experiments conducted on images issued from 7 different DR systems show first it is possible to identify with good accuracy the origin of one DR image and, second, that contourlet filtering leads to better detection performance than commonly used approaches based on wavelet or BM3D filtering.

As one of the most important image segmentation models, the Mumford-Shah functional was developed to pursue a piecewise smooth approximation of a given image based on the regularization on the total length of curves. In this paper, we modify the Mumford-Shah model using Euler's elastic a as the regularization. A two-stage segmentation method is applied the Euler's elastic a regularized Mumford-Shah model. The first stage is to find a smooth solution of the variant Mumford-Shah functional based on augmented Lagrangian method while a thresholding is performed in the second stage to obtain different phases for the segmentation. The K-means clustering method is used as the technique to find the thresholds for the segmentation. For intensity inhomogeneous images, we eliminate the effect of the bias field by bias-corrected fuzzy c-means method. Experimental results show that as the regularization, Euler's elastic a makes the Mumford-Shah model perform better for many kinds of images, including tubular and irregular shaped, CT Angiography (CTA) and MRI images in different noise level.