arXiv subjects

Zongming Guo

Publications and source records attributed to Zongming Guo.

39 records · Page 3Linked to original sources

arXiv2016

Deep Edge Guided Recurrent Residual Learning for Image Super-Resolution

In this work, we consider the image super-resolution (SR) problem. The main challenge of image SR is to recover high-frequency details of a low-resolution (LR) image that are important for human perception. To address this essentially ill-posed problem, we introduce a Deep Edge Guided REcurrent rEsidual~(DEGREE) network to progressively recover the high-frequency details. Different from most of existing methods that aim at predicting high-resolution (HR) images directly, DEGREE investigates an alternative route to recover the difference between a pair of LR and HR images by recurrent residual learning. DEGREE further augments the SR process with edge-preserving capability, namely the LR image and its edge map can jointly infer the sharp edge details of the HR image during the recurrent recovery process. To speed up its training convergence rate, by-pass connections across multiple layers of DEGREE are constructed. In addition, we offer an understanding on DEGREE from the view-point of sub-band frequency decomposition on image signal and experimentally demonstrate how DEGREE can recover different frequency bands separately. Extensive experiments on three benchmark datasets clearly demonstrate the superiority of DEGREE over well-established baselines and DEGREE also provides new state-of-the-arts on these datasets.

cs.CV↗

arXiv2016

MARLow: A Joint Multiplanar Autoregressive and Low-Rank Approach for Image Completion

In this paper, we propose a novel multiplanar autoregressive (AR) model to exploit the correlation in cross-dimensional planes of a similar patch group collected in an image, which has long been neglected by previous AR models. On that basis, we then present a joint multiplanar AR and low-rank based approach (MARLow) for image completion from random sampling, which exploits the nonlocal self-similarity within natural images more effectively. Specifically, the multiplanar AR model constraints the local stationarity in different cross-sections of the patch group, while the low-rank minimization captures the intrinsic coherence of nonlocal patches. The proposed approach can be readily extended to multichannel images (e.g. color images), by simultaneously considering the correlation in different channels. Experimental results demonstrate that the proposed approach significantly outperforms state-of-the-art methods, even if the pixel missing rate is as high as 90%.

cs.CV↗

arXiv2013

Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations

By introducing a suitable setting, we study the behavior of finite Morse index solutions of the equation \[ -\{div} (|x|^θ\nabla v)=|x|^l |v|^{p-1}v \;\;\; \{in $Ω\subset \R^N \; (N \geq 2)$}, \leqno(1) \] where $p>1$, $θ, l\in\R^1$ with $N+θ>2$, $l-θ>-2$, and $Ω$ is a bounded or unbounded domain. Through a suitable transformation of the form $v(x)=|x|^σu(x)$, equation (1) can be rewritten as a nonlinear Schrödinger equation with Hardy potential $$-Δu=|x|^α|u|^{p-1}u+\frac{\ell}{|x|^2} u \;\; \{in $Ω\subset \R^N \;\; (N \geq 2)$}, \leqno{(2)}$$ where $p>1$, $α\in (-\infty, \infty)$ and $\ell \in (-\infty,(N-2)^2/4)$. We show that under our chosen setting for the finite Morse index theory of (1), the stability of a solution to (1) is unchanged under various natural transformations. This enables us to reveal two critical values of the exponent $p$ in (1) that divide the behavior of finite Morse index solutions of (1), which in turn yields two critical powers for (2) through the transformation. The latter appear difficult to obtain by working directly with (2).

math.AP↗