Zhi Wang

Wendong Wang, Feng Zhang, Zhi Wang et al.

In this paper, we consider recovering the signal $\bm{x}\in\mathbb{R}^{n}$ from its few noisy measurements $\bm{b}=A\bm{x}+\bm{z}$, where $A\in\mathbb{R}^{m\times n}$ with $m\ll n$ is the measurement matrix, and $\bm{z}\in\mathbb{R}^{m}$ is the measurement noise/error. We first establish a coherence-based performance guarantee for a regularized $\ell_{1}$-norm minimization model to recover such signals $\bm{x}$ in the presence of the $\ell_{2}$-norm bounded noise, i.e., $\|\bm{z}\|_{2}\leqε$, and then extend these theoretical results to guarantee the robust recovery of the signals corrupted with the Dantzig Selector (DS) type noise, i.e., $\|A^{T}\bm{z}\|_{\infty}\leqε$, and the structured block-sparse signal recovery in the presence of the bounded noise. To the best of our knowledge, we first extend nontrivially the sharp uniform recovery condition derived by Cai, Wang and Xu (2010) for the constrained $\ell_{1}$-norm minimization model, which takes the form of \begin{align*} μ<\frac{1}{2k-1}, \end{align*} where $μ$ is defined as the (mutual) coherence of $A$, to two unconstrained regularized $\ell_{1}$-norm minimization models to guarantee the robust recovery of any signals (not necessary to be $k$-sparse) under the $\ell_{2}$-norm bounded noise and the DS type noise settings, respectively. Besides, a uniform recovery condition and its two resulting error estimates are also established for the first time to our knowledge, for the robust block-sparse signal recovery using a regularized mixed $\ell_{2}/\ell_{1}$-norm minimization model, and these results well complement the existing theoretical investigation on this model which focuses on the non-uniform recovery conditions and/or the robust signal recovery in presence of the random noise.

Wei Yao, Shuzhao Xie, Letian Li et al.

Current 4D Gaussian frameworks for dynamic scene reconstruction deliver impressive visual fidelity and rendering speed, however, the inherent trade-off between storage costs and the ability to characterize complex physical motions significantly limits the practical application of these methods. To tackle these problems, we propose SD-GS, a compact and efficient dynamic Gaussian splatting framework for complex dynamic scene reconstruction, featuring two key contributions. First, we introduce a deformable anchor grid, a hierarchical and memory-efficient scene representation where each anchor point derives multiple 3D Gaussians in its local spatiotemporal region and serves as the geometric backbone of the 3D scene. Second, to enhance modeling capability for complex motions, we present a deformation-aware densification strategy that adaptively grows anchors in under-reconstructed high-dynamic regions while reducing redundancy in static areas, achieving superior visual quality with fewer anchors. Experimental results demonstrate that, compared to state-of-the-art methods, SD-GS achieves an average of 60\% reduction in model size and an average of 100\% improvement in FPS, significantly enhancing computational efficiency while maintaining or even surpassing visual quality.