3D Gaussian Splatting (3DGS) has revolutionized novel view synthesis with real-time rendering and high-quality reconstruction. However, its performance degrades under varying scales, causing aliasing and dilation artifacts. To address these challenges, we introduce Msa-Splatting, an enhanced adaptive Gaussian splatting method designed for high-fidelity multi-scale novel view synthesis. Our approach reimagines the Gaussian adaptive control process with a novel multi-fold splitting and cloning mechanism, which optimizes Gaussian properties and reduces spurious artifacts by halving the densification frequency. We further mitigate aliasing in scaled-down renderings with a weighted alpha blending sampling technique, ensuring accurate representation of high-frequency details. To eliminate scale-mismatch artifacts, we introduce 2D variable dilation Gaussians, which dynamically adjust dilation based on the rendering scale. Msa-Splatting significantly enhances the fidelity and adaptability of Gaussian-based rendering, achieving state-of-the-art performance in multi-scale novel view synthesis. Extensive quantitative and qualitative evaluations demonstrate the efficacy of our approach, showcasing its ability to produce perceptually superior renderings with reduced artifacts across varying scales, thus establishing a robust framework for future advancements in scalable rendering technologies.

Deep convolutional neural networks have significantly advanced color image denoising. However, existing models often apply grayscale denoising techniques to color images without accounting for inter-channel correlations, resulting in color distortion, detail loss, and visual artifacts. Moreover, these models frequently neglect salient features within convolutional maps. To address these issues, we propose a quaternion CNN model that captures channel correlations and extracts salient features, thereby enhancing color image denoising performance. Specifically, we convert color images into quaternion matrices to better capture these correlations and design a quaternion convolutional network to learn relevant features. Furthermore, an aggregated feature block is introduced to enhance the extraction of salient features and further refine the denoising process. Experimental results on multiple datasets demonstrate that the proposed model achieves superior performance compared to recent state-of-the-art methods.

Transformer-based methods have achieved notable success in image deraining because of the ability of dot-product self-attention to capture long-range dependencies. However, the quadratic computational complexity of dot-product self-attention limits its scalability for large images. In this paper, we introduce SSAformer, a simplified synthetic attention Transformer model, to address this issue. SSAformer comprises two key components: (1) a simplified synthetic attention solver (SSAS), which reduces computational complexity by constructing a synthetic attention matrix independent of token-token dependencies, and (2) a simple discriminative feed-forward network (SDFN), which uses a learnable quantization matrix to selectively retain crucial features for image restoration. This approach achieves linear computational complexity, greatly enhancing efficiency for large-scale images. Extensive experiments on synthetic and real-world datasets demonstrate that SSAformer outperforms state-of-the-art methods in both quantitative and qualitative evaluations, showcasing its effectiveness and efficiency for image deraining.

Sparse view computed tomography (CT) reconstruction poses a challenging ill-posed inverse problem, necessitating effective regularization techniques. In this letter, we employ$L_{p}$-norm ($0< p< 1$) regularization to induce sparsity and introduce inertial steps, leading to the development of the inertial$L_{p}$-norm half-quadratic splitting algorithm. We rigorously prove the convergence of this algorithm. Furthermore, we leverage deep learning to initialize the conjugate gradient method, resulting in a deep unrolling network with theoretical guarantees. Our extensive numerical experiments demonstrate that our proposed algorithm surpasses existing methods, particularly excelling in fewer scanned views and complex noise conditions.

Image denoising is one of the most important tasks in image processing. In this paper, we study image denoising methods by using similar patches which have low-rank covariance matrices to recover an underlying image which is corrupted by additive Gaussian noise. In order to enhance global patch-matching results, we make use of a Gaussian mixture model with an auxiliary image to determine different groups of patches. The auxiliary image is an output of BM3D. The noisy version of covariance matrix is formed by each group of patches from the given noisy image. Its low-rank version can be estimated by using covariance matrix nuclear norm minimization, and the resulting denoised image can be obtained. Experimental results are reported to show that the proposed method outperforms the state-of-the-art denoising methods, including testing deep learning methods, in the peak signal-to-noise ratio, structural similarity values, and visual quality.

The image nonlocal self-similarity (NSS) prior refers to the fact that a local patch often has many nonlocal similar patches to it across the image and has been widely applied in many recently proposed machining learning algorithms for image processing. However, there is no theoretical analysis on its working principle in the literature. In this paper, we discover a potential causality between NSS and low-rank property of color images, which is also available to grey images. A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images. The numerical low-rank property of patched matrices is also rigorously proved. The NSS-based QMC algorithm computes an optimal low-rank approximation to the high-rank color image, resulting in high PSNR and SSIM measures and particularly the better visual quality. A new tensor NSS-based QMC method is also presented to solve the color video inpainting problem based on quaternion tensor representation. The numerical experiments on color images and videos indicate the advantages of NSS-based QMC over the state-of-the-art methods.

With the widespread application of convolutional neural networks (CNNs), the traditional model based denoising algorithms are now outperformed. However, CNNs face two problems. First, they are computationally demanding, which makes their deployment especially difficult for mobile terminals. Second, experimental evidence shows that CNNs often over-smooth regular textures present in images, in contrast to traditional non-local models. In this letter, we propose a solution to both issues by combining a nonlocal algorithm with a lightweight residual CNN. s solution gives full latitude to the advantages of both models. We apply this framework to two GPU implementations of classic nonlocal algorithms (NLM and BM3D) and observe a substantial gain in both cases, performing better than the state-of-the-art with low computational requirements. Our solution is between 10 and 20 times faster than CNNs with equivalent performance and attains higher PSNR. In addition the final method shows a notable gain on images containing complex textures like the ones of the MIT Moiré dataset.

This study describes an improved method for Poisson image denoising that is based on a state‐of‐the‐art Poisson denoising approach known as non‐local principal component analysis (NLPCA). The new method is referred to as PieceWise Principal Component Analysis (PWPCA). In PWPCA, the given image is first split into pieces, then NLPCA is run on each image piece, and finally the entire image is reconstituted by a weighted combination of the NLPCA‐processed image pieces. Using standard test images with Poisson noise, the authors show that PWPCA restores images more effectively than state‐of‐the‐art Poisson denoising approaches. In addition, and to the best of their knowledge, they show the first application of such approaches to single‐particle X‐ray free‐electron laser (XFEL) data. They show that the resolution of three‐dimensional reconstruction from XFEL diffraction images is improved when the data are preprocessed with PWPCA. XFELs are currently under rapid development to allow high‐resolution biomolecular structure determination at near‐physiological conditions. Data analysis methods developments follow these technological advances and are expected to have high impact in structural biology and drug design. This study contributes to these developments. As little experimental single‐particle XFEL data is available still, the XFEL experiments shown here were performed with simulated data.

In this paper, a new denoising algorithm to deal with the additive white Gaussian noise model is described. Following the nonlocal (NL) means approach, we propose an adaptive estimator based on the weighted average of observations taken in a neighborhood with weights depending on the similarity of local patches. The idea is to compute adaptive weights that best minimize an upper bound of the pointwise $L_2$ risk. In the framework of adaptive estimation, we show that the “oracle” weights are optimal if we consider triangular kernels instead of the commonly used Gaussian kernel. Furthermore, we propose a way to automatically choose the spatially varying smoothing parameter for adaptive denoising. Under conventional minimal regularity conditions, the obtained estimator converges at the usual optimal rate. The implementation of the proposed algorithm is also straightforward and the simulations show that our algorithm significantly improves the classical NL means and is competitive when compared to the more sophisticated NL means filters, both in terms of peak signal-to-noise ratio values and visual quality.

Structural changes are critical for biological functions of proteins and describing conformational changes in large macromolecular complexes is a major challenge. We have recently developed a hybrid method (HEMNMA) combining transmission electron microscopy (EM), normal mode analysis (NMA), and image analysis to study macromolecular dynamics. NMA is traditionally used to study macromolecular motions while HEMNMA provides insight into actual conformational changes seen by EM. HEMNMA uses normal modes to elastically align EM images with a reference structure in order to determine the conformations present in images and evaluate their pertinence. In this paper, we show how HEMNMA can be used with an atomic-resolution reference structure, using as an example the study of the conformational dynamics of Tomato Bushy Stunt Virus.