Digital photography image fusion aims to integrate essential information from multiple source images. However, the current methods predominantly rely on a single-channel fusion strategy, failing to fully leverage color pixel information. Furthermore, the significant variations in fusion mechanisms across tasks limit the performance of generic models. These factors can lead to color shifts and the loss of fine details. To address these issues, we propose a novel approach named MRQE-Net for general digital photography image fusion. The proposed network treats RGB pixels as a unified entity by encapsulating them into reduced biquaternion (RQ), and achieves task-specific fusion through mixture of RQ experts (MoRQE) module within a unified model. Specifically, we first develop the RQ spatial attention (RQSA) and RQ multi-scale pixel attention (RQMSPA) modules to enhance salient features. Then, we propose the deep feature invertible module (DFIM) to efficiently extract the complementary deep information. Finally, to enable customized fusion and feature enhancement for each task, we propose the adaptive feature synthesis amplification module (AFSAM). To the best of our knowledge, this is the first attempt to perform digital photography image fusion in RQ neural networks. Extensive experiments demonstrate that the MRQE-Net outperforms state-of-the-art methods across multiple metrics for each subtask.

Real-valued wavelets have achieved great success in image denoising due to their sparse representation capability under multi-scale analysis. However, existing real-valued wavelets suffer from limited directional selectivity and translation sensitivity, which can lead to color distortion and loss of phase information. The quaternion wavelet transform (QWT) offers a new solution by extending each pair of complex filters in the dual-tree complex wavelet transform to quaternion-valued filter banks, generating quaternion high frequency subbands in three principal directions while retaining a low frequency approximation, thus achieving cross channel translation invariance and phase consistency. Based on this, we propose a QWT-driven multi-scale feature interaction network (QMFINet). QMFINet leverages QWT to extract cross channel structured phase features at the same spatial locations, precisely linking color and texture details; it further employs a three-path feature extraction module (TPFEM) to capture multi-scale representations. To effectively fuse features at different resolutions, we design a quaternion ordered channel attention subnet (QOCAS). Experimental results demonstrate that QMFINet outperforms several state-of-the-art color image denoising methods across a range of noise levels, and achieves the best performance at$\sigma =75$, with an average PSNR improvement of approximately 0.3-0.4 dB over the previous state-of-the-art method.

As a prerequisite for many vision-oriented tasks, image deraining is an effective solution to alleviate performance degradation of these tasks on rainy days. In recent years, the introduction of deep learning has obtained the significant developments in deraining techniques. However, due to the inherent constraints of synthetic datasets and the insufficient robustness of network architecture designs, most existing methods are difficult to fit varied rain patterns and adapt to the transition from synthetic rainy images to real ones, ultimately resulting in unsatisfactory restoration outcomes. To address these issues, we propose a reduced biquaternion dual-branch deraining U-Network (RQ-D2UNet) for better deraining performance, which is the first attempt to apply the reduced biquaternion-valued neural network in the deraining task. The algebraic properties of reduced biquaternion (RQ) can facilitate modeling the rainy artifacts more accurately while preserving the underlying spatial structure of the background image. The comprehensive design scheme of U-shaped architecture and dual-branch structure can extract multi-scale contextual information and fully explore the mixed correlation between rain and rain-free features. Moreover, we also extend the self-attention and convolutional attention mechanisms in the RQ domain, which allow the proposed model to balance both global dependency capture and local feature extraction. Extensive experimental results on various rainy datasets (i.e., rain streak/rain-haze/raindrop/real rain), downstream vision applications (i.e., object detection and segmentation), and similar image restoration tasks (i.e., image desnowing and low-light image enhancement) demonstrate the superiority and versatility of our proposed method.

The existing deraining methods are based on convolutional neural networks (CNN) learning the mapping relationship between rainy and clean images. However, the real-valued CNN processes the color images as three independent channels separately, which fails to fully leverage color information. Additionally, sliding-window-based neural networks cannot effectively model the non-local characteristics of an image. In this work, we proposed a non-local feature aggregation quaternion network (NLAQNet), which is composed of two concurrent sub-networks: the Quaternion Local Detail Repair Network (QLDRNet) and the Multi-Level Feature Aggregation Network (MLFANet). Furthermore, in the subnetwork of QLDRNet, the Local Detail Repair Block (LDRB) is proposed to repair the backdrop of an image that has not been damaged by rain streaks. Finally, within the MLFANet subnetwork, we have introduced two specialized blocks, namely the Non-Local Feature Aggregation Block (NLAB) and the Feature Aggregation Block (Mix), specifically designed to address the restoration of rain-streak-damaged image backgrounds. Extensive experiments demonstrate that the proposed network delivers strong performance in both qualitative and quantitative evaluations on existing datasets. The code is available at https://github.com/xionggonghe/NLAQNet .

The reduced biquaternion-valued neural network (RQV-CNN) has recently seen tremendous success for color image processing. However, existing RQV-CNNs are relatively simple in structure and lack effective components, limiting the potential to enhance their performance. Furthermore, an effective method is needed to improve the unsatisfactory denoising results of RQV-CNNs in hard scenes. Therefore, we conduct an in-depth study in the RQ domain and propose a new denoising method, namely RQUNet. To our best knowledge, our approach is the first attempt to construct RQ deconvolutional layer. Building upon this, we construct a deeper RQ network. Additionally, we propose a parallel reduced biquaternion dual attention module to enhance the denoising performance of RQ network in hard scenes. RQUNet is entirely composed of reduced biquaternion-valued blocks, which achieve a significant reduction in the number of parameters. Extensive color image denoising experiments on three different denoising datasets demonstrate that our model achieved the highest average PSNR of 30.66 dB, which surpassed the previous state-of-the-art method by 0.28 dB with less computational cost, and obtained better visualization results.

Image rain removal is an essential problem of common concern in the fields of image processing and computer vision. Existing methods have resorted to deep learning techniques to separate rain streaks from the background by leveraging some prior knowledge. However, the mismatch between the size of the rain streaks during the training and testing phases, especially when large rain streaks are present, frequently leads to unsatisfactory deraining results. To address this issue, we propose a multi-scale self-calibrated dual attention lightweight residual dense deraining network (MDARNet) for better deraining performance. Specifically, the network consists of monogenic wavelet transform-like hierarchy and self-calibrated dual attention mechanism. With the help of scale-space properties of the monogenic wavelet transform, key features at different scales can be extracted at the same location, which makes it easier to match structural features across scales. The self-calibrated double attention mechanism was used as a basic model for enhancing the channel dependence and spatial correlation between each layer component of the monogenic wavelet transform. Thus, the network can establish long-range dependencies and take advantage of rich contextual information and multi-scale redundancy to accommodate rain streaks of different shapes and sizes. Experiments on synthetic and real image datasets show that the method outperforms many of the latest single-image deraining methods in terms of visual and quantitative metrics. The source code can be obtained fromhttps://github.com/smart-hzw/MDARNet.

Reduced biquaternion is a four dimensional hyper–complex number which is commutative algebra and an extension of complex. Due to this property, the corresponding fast algorithm is designed in time frequency analysis which can better fit the convolution theorem than the non-commutative quaternion. In addition, the reduced biquaternion can be interpreted as a single point in 2-dimensional hyperbolic space with its algebraic structure which has more capacity and variable ability than the Euclidean space. However, the algebra properties of the reduced biquaternion have not yet been well explored in the deep convolutional neural network. In this paper, we develop a new deep network structure, namely reduced biquaternion valued convolutional neural network (RQV-CNN). The proposed RQV-CNN includes basic modules of reduced biquaternion convolution layer and fully connection layer. Extensive experiments on color image classification and color image denoising are conducted to evaluate the promising performance of the RQV-CNN framework. The results show that RQV-CNN outperforms the real-valued CNN (RV-CNN), complex-valued CNN (CV-CNN), and quaternion-valued CNN (QV-CNN) with same structures. The source code can be found athttps://github.com/tasteimage/RQVCNN.

RGB-D image classification based on convolutional neural networks have been extensively explored recently. However, they suffer from problems of effective representation of RGB-D image, intra-class variances and inter-class similarities. To address these problems, this letter proposes a novel RGB-D image classification framework based on reduced biquaternion stacked denoising convolutional autoencoder (RQ-SDCAE). The proposed framework can encode and extract the depth feature effectively by using the reduced biquaternion. The stacked training method is utilized to train the proposed reduced biquaternion convolutional autoencoder. Extensive evaluations for RGB-D image classification demonstrate that RQ-SDCAE outperforms the state-of-the-art methods.

The traditional colour image sparse models ignore the relationship among the three separate colour channels. The authors propose a novel colour image sparse model by employing reduced quaternion matrix, which can treat independent colour channels as a whole. In addition, reduced quaternion matrix singular value decomposition is employed to design the corresponding dictionary learning algorithm. To make the proposed model robust and tractable, a reduced quaternion split Bregman iteration is developed to solve the minimisation problem. The proposed model cannot only preserve inherent colour structures but also avoid hue bias issue efficiently. Extensive experiments on colour image de‐noising, in‐painting, and super‐resolution manifest that the proposed sparse representation model outperforms the state‐of‐the‐art schemes.

In this study, the authors study and give a new framework for colour image representation based on colour quaternion wavelet transform (CQWT). The new colour quaternion filter bank is constructed by using radon transform. Starting from link with structure tensors, the authors propose a new multi‐scale tool for vector‐valued signals which can provide efficient analysis of local features by using the concepts of amplitude, phase, and orientation. To demonstrate the properties of CQWT, new colour image denoising algorithm is proposed by using CQWT and bivariate shrinkage function. The performance of the proposed algorithm is experimentally verified on a variety of noise levels. Experimental results show that the proposed algorithm achieves superior performance both in visual quality and objective peak‐signal‐to‐noise ratio, mean square error, and structure similarity values, compared with other state‐of‐the‐art denoising algorithms.

Sparse representations of multi‐channel signals have drawn considerable interest in recent years. In this study, a new vector‐valued sparse representation model is proposed for colour images using reduced quaternion matrix (RQM). The colour image is described as a RQM by the proposed model. In the dictionary training state, k ‐means clustering RQM value decomposition is proposed which makes sparse basis selection in quaternion space. Then, a reduced quaternion‐based orthogonal matching pursuit algorithm is presented in the sparse coding stage. To demonstrate the effectiveness of the proposed sparse representation model, the authors apply the model to common colour image processing problem‐colour image denoising. The proposed model is compared with other sparse models for colour image denoising in terms of visual quality and peak signal‐to‐noise ratio. The experimental results indicate that the proposed image sparse model is competitive with other sparse models.