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Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field $\mathbb{F}_{p^m}$. Through the utilization of CSS and Steane's constructions, a series of new quantum error-correcting (QEC) codes are constructed with parameters distinct from all previous constructions. Furthermore, we provide all maximum distance separable (MDS) cyclic codes of length $2^rp^s$, which are further utilized in the construction of QEC MDS codes. Finally, we introduce a significant number of novel entanglement-assisted quantum error-correcting (EAQEC) codes derived from these repeated-root cyclic codes. Notably, these newly constructed codes exhibit parameters distinct from those of previously known constructions.

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 infection 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 sweet balance of regularization functionals 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 infection 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 manoeuvrability 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., Comment: 15pages,10figures

Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good minimum distance. In this paper, by using the BCH bound on cyclic codes, one of the open problems proposed by Liu et al. about binary cyclic codes (Finite Field Appl 91:102270, 2023) is settled. Specially, we present several families of binary duadic codes with length 2^m-1 and dimension 2^(m-1), and the minimum distances have a square-root-like lower bound. As a by-product, the parameters of their dual codes and extended codes are provided, where the latter are self-dual and doubly-even., Comment: 15 pages

Recovering clear images from blurry ones with an unknown blur kernel is a challenging problem. Deep image prior (DIP) proposes to use the deep network as a regularizer for a single image rather than as a supervised model, which achieves encouraging results in the nonblind deblurring problem. However, since the relationship between images and the network architectures is unclear, it is hard to find a suitable architecture to provide sufficient constraints on the estimated blur kernels and clean images. Also, DIP uses the sparse maximum a posteriori (MAP), which is insufficient to enforce the selection of the recovery image. Recently, variational deep image prior (VDIP) was proposed to impose constraints on both blur kernels and recovery images and take the standard deviation of the image into account during the optimization process by the variational principle. However, we empirically find that VDIP struggles with processing image details and tends to generate suboptimal results when the blur kernel is large. Therefore, we combine total generalized variational (TGV) regularization with VDIP in this paper to overcome these shortcomings of VDIP. TGV is a flexible regularization that utilizes the characteristics of partial derivatives of varying orders to regularize images at different scales, reducing oil painting artifacts while maintaining sharp edges. The proposed VDIP-TGV effectively recovers image edges and details by supplementing extra gradient information through TGV. Additionally, this model is solved by the alternating direction method of multipliers (ADMM), which effectively combines traditional algorithms and deep learning methods. Experiments show that our proposed VDIP-TGV surpasses various state-of-the-art models quantitatively and qualitatively., Comment: 13 pages, 5 figures

Fluorescent molecules are versatile nanoscale emitters that enable detailed observations of biophysical processes with nanoscale resolution. Because they are well-approximated as electric dipoles, imaging systems can be designed to visualize their 3D positions and 3D orientations, so-called dipole-spread function (DSF) engineering, for 6D super-resolution single-molecule orientation-localization microscopy (SMOLM). We review fundamental image-formation theory for fluorescent di-poles, as well as how phase and polarization modulation can be used to change the image of a dipole emitter produced by a microscope, called its DSF. We describe several methods for designing these modulations for optimum performance, as well as compare recently developed techniques, including the double-helix, tetrapod, crescent, and DeepSTORM3D learned point-spread functions (PSFs), in addition to the tri-spot, vortex, pixOL, raPol, CHIDO, and MVR DSFs. We also cover common imaging system designs and techniques for implementing engineered DSFs. Finally, we discuss recent biological applications of 6D SMOLM and future challenges for pushing the capabilities and utility of the technology., Comment: This is a preprint of the following chapter: Tingting Wu and Matthew D. Lew, Dipole-Spread Function Engineering for 6D Super-Resolution Microscopy, published in Coded optical imaging, edited by Jinyang Lang, 2023, Springer Nature reproduced with permission of Springer Nature

Large-scale datasets in the real world inevitably involve label noise. Deep models can gradually overfit noisy labels and thus degrade model generalization. To mitigate the effects of label noise, learning with noisy labels (LNL) methods are designed to achieve better generalization performance. Due to the lack of suitable datasets, previous studies have frequently employed synthetic label noise to mimic real-world label noise. However, synthetic noise is not instance-dependent, making this approximation not always effective in practice. Recent research has proposed benchmarks for learning with real-world noisy labels. However, the noise sources within may be single or fuzzy, making benchmarks different from data with heterogeneous label noises in the real world. To tackle these issues, we contribute NoisywikiHow, the largest NLP benchmark built with minimal supervision. Specifically, inspired by human cognition, we explicitly construct multiple sources of label noise to imitate human errors throughout the annotation, replicating real-world noise, whose corruption is affected by both ground-truth labels and instances. Moreover, we provide a variety of noise levels to support controlled experiments on noisy data, enabling us to evaluate LNL methods systematically and comprehensively. After that, we conduct extensive multi-dimensional experiments on a broad range of LNL methods, obtaining new and intriguing findings., Comment: The paper has been accepted by ACL 2023 Findings. Dataset and code are available in this https URL

Federated learning (FL) is an emerging paradigm to train model with distributed data from numerous Internet of Things (IoT) devices. It inherently assumes a uniform capacity among participants. However, due to different conditions such as differing energy budgets or executing parallel unrelated tasks, participants have diverse computational resources in practice. Participants with insufficient computation budgets must plan for the use of restricted computational resources appropriately, otherwise they would be unable to complete the entire training procedure, resulting in model performance decline. To address this issue, we propose a strategy for estimating local models without computationally intensive iterations. Based on it, we propose Computationally Customized Federated Averaging (CC-FedAvg), which allows participants to determine whether to perform traditional local training or model estimation in each round based on their current computational budgets. Both theoretical analysis and exhaustive experiments indicate that CC-FedAvg has the same convergence rate and comparable performance as FedAvg without resource constraints. Furthermore, CC-FedAvg can be viewed as a computation-efficient version of FedAvg that retains model performance while considerably lowering computation overhead., Comment: 16 pages, 10 figures

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: i) 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; ii) Deep learning is notoriously a black-box model [1]. It is difficult to explain their inner-working mechanism and understand their behaviors. In this paper, using a sequential Retinex decomposition strategy, we design a plug-and-play framework based on the Retinex theory for simultaneously 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 enhanced image is produced 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.

Given data with label noise (i.e., incorrect data), deep neural networks would gradually memorize the label noise and impair model performance. To relieve this issue, curriculum learning is proposed to improve model performance and generalization by ordering training samples in a meaningful (e.g., easy to hard) sequence. Previous work takes incorrect samples as generic hard ones without discriminating between hard samples (i.e., hard samples in correct data) and incorrect samples. Indeed, a model should learn from hard samples to promote generalization rather than overfit to incorrect ones. In this paper, we address this problem by appending a novel loss function DiscrimLoss, on top of the existing task loss. Its main effect is to automatically and stably estimate the importance of easy samples and difficult samples (including hard and incorrect samples) at the early stages of training to improve the model performance. Then, during the following stages, DiscrimLoss is dedicated to discriminating between hard and incorrect samples to improve the model generalization. Such a training strategy can be formulated dynamically in a self-supervised manner, effectively mimicking the main principle of curriculum learning. Experiments on image classification, image regression, text sequence regression, and event relation reasoning demonstrate the versatility and effectiveness of our method, particularly in the presence of diversified noise levels.

We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the $\ell_0$ norm under a tight framelet system as a regularization to promote sparsity. This model leads to a non-smooth, non-convex optimization problem for which traditional iteration schemes are inefficient or even divergent. By exploiting special structures of the $\ell_0$ norm, we identify a local minimizer of the proposed non-convex optimization problem with a global minimizer of a convex optimization problem, which provides us insights for the development of efficient and convergence guaranteed algorithms to solve it. We characterize the solution of the regularization model in terms of a fixed-point of a map defined by the proximity operator of the $\ell_0$ norm and develop a fixed-point iteration algorithm to solve it. By connecting the map with an $\alpha$-averaged nonexpansive operator, we prove that the sequence generated by the proposed fixed-point proximity algorithm converges to a local minimizer of the proposed model. Our numerical examples confirm that the proposed model outperforms significantly the existing model based on the $\ell_1$-norm. The seismic wavefield modeling in the frequency domain requires solving a series of the Helmholtz equation with large wave numbers, which is a computationally intensive task. Applying the proposed sparse regularization model to the seismic wavefield modeling requires data of only a few low frequencies, avoiding solving the Helmholtz equation with large wave numbers. Numerical results show that the proposed method performs better than the existing method based on the $\ell_1$ norm in terms of the SNR values and visual quality of the restored synthetic seismograms.

As an emerging technology, federated learning (FL) involves training machine learning models over distributed edge devices, which attracts sustained attention and has been extensively studied. However, the heterogeneity of client data severely degrades the performance of FL compared with that in centralized training. It causes the locally trained models of clients to move in different directions. On the one hand, it slows down or even stalls the global updates, leading to inefficient communication. On the other hand, it enlarges the distances between local models, resulting in an aggregated global model with poor performance. Fortunately, these shortcomings can be mitigated by reducing the angle between the directions that local models move in. Based on this fact, we propose FedCos, which reduces the directional inconsistency of local models by introducing a cosine-similarity penalty. It promotes the local model iterations towards an auxiliary global direction. Moreover, our approach is auto-adapt to various non-IID settings without an elaborate selection of hyperparameters. The experimental results show that FedCos outperforms the well-known baselines and can enhance them under a variety of FL scenes, including varying degrees of data heterogeneity, different number of participants, and cross-silo and cross-device settings. Besides, FedCos improves communication efficiency by 2 to 5 times. With the help of FedCos, multiple FL methods require significantly fewer communication rounds than before to obtain a model with comparable performance., Comment: 11 pages, 13 figures