Yu Guo

Yu Guo, Guoqing Chen, Tieyong Zeng et al.

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.

Zhenyuan Liu, Yu Guo, Xinyuan Li et al.

We present Bidirectional Gaussian Primitives, an image-based novel view synthesis technique designed to represent and render 3D objects with surface and volumetric materials under dynamic illumination. Our approach integrates light intrinsic decomposition into the Gaussian splatting framework, enabling real-time relighting of 3D objects. To unify surface and volumetric material within a cohesive appearance model, we adopt a light- and view-dependent scattering representation via bidirectional spherical harmonics. Our model does not use a specific surface normal-related reflectance function, making it more compatible with volumetric representations like Gaussian splatting, where the normals are undefined. We demonstrate our method by reconstructing and rendering objects with complex materials. Using One-Light-At-a-Time (OLAT) data as input, we can reproduce photorealistic appearances under novel lighting conditions in real time.

Yu Guo, Caiying Wu, Yaxin Li et al.

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.

Yu Guo, Axel Davy, Gabriele Facciolo et al.

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. This 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 Moire dataset.

Yu Guo, Guoqing Chen, Tieyong Zeng et al.

Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model multi-dimensional data, offer a promising framework for this problem. This paper introduces the quaternion nuclear norm over the Frobenius norm (QNOF) as a novel nonconvex approximation for the rank of quaternion matrices. QNOF is parameter-free and scale-invariant. Utilizing quaternion singular value decomposition, we prove that solving the QNOF can be simplified to solving the singular value $L_1/L_2$ problem. Additionally, we extend the QNOF to robust quaternion matrix completion, employing the alternating direction multiplier method to derive solutions that guarantee weak convergence under mild conditions. Extensive numerical experiments validate the proposed model's superiority, consistently outperforming state-of-the-art quaternion methods.