Yang Chen

Prathapasinghe Dharmawansa, Matthew McKay, Yang Chen

Consider a random matrix $\mathbf{A}\in\mathbb{C}^{m\times n}$ ($m \geq n$) containing independent complex Gaussian entries with zero mean and unit variance, and let $0<λ_1\leq λ_{2}\leq ...\leq λ_n<\infty$ denote the eigenvalues of $\mathbf{A}^{*}\mathbf{A}$ where $(\cdot)^*$ represents conjugate-transpose. This paper investigates the distribution of the random variables $\frac{\sum_{j=1}^n λ_j}{λ_k}$, for $k = 1$ and $k = 2$. These two variables are related to certain condition number metrics, including the so-called Demmel condition number, which have been shown to arise in a variety of applications. For both cases, we derive new exact expressions for the probability densities, and establish the asymptotic behavior as the matrix dimensions grow large. In particular, it is shown that as $n$ and $m$ tend to infinity with their difference fixed, both densities scale on the order of $n^3$. After suitable transformations, we establish exact expressions for the asymptotic densities, obtaining simple closed-form expressions in some cases. Our results generalize the work of Edelman on the Demmel condition number for the case $m = n$.

Wenbin Li, Yang Chen, JeeHang Lee et al.

It is hard to estimate optical flow given a realworld video sequence with camera shake and other motion blur. In this paper, we first investigate the blur parameterization for video footage using near linear motion elements. we then combine a commercial 3D pose sensor with an RGB camera, in order to film video footage of interest together with the camera motion. We illustrates that this additional camera motion/trajectory channel can be embedded into a hybrid framework by interleaving an iterative blind deconvolution and warping based optical flow scheme. Our method yields improved accuracy within three other state-of-the-art baselines given our proposed ground truth blurry sequences; and several other realworld sequences filmed by our imaging system.