This paper presents a new patch-based video restoration scheme. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and low-rank matrix approximation problem. The resulting nuclear norm and $\ell_1$ norm related minimization problem can also be efficiently solved by many recently developed numerical methods. The effectiveness of the proposed video restoration scheme is illustrated on two applications: video denoising in the presence of random-valued noise, and video in-painting for archived films. The numerical experiments indicate that the proposed video restoration method compares favorably against many existing algorithms.

A texture descriptor is proposed, which combines local highly discriminative features with the global statistics of fractal geometry to achieve high descriptive power, but also invariance to geometric and illumination transformations. As local measurements SIFT features are estimated densely at multiple window sizes and discretized. On each of the discretized measurements the fractal dimension is computed to obtain the so-called multifractal spectrum, which is invariant to geometric transformations and illumination changes. Finally to achieve robustness to scale changes, a multi-scale representation of the multifractal spectrum is developed using a framelet system, that is, a redundant tight wavelet frame system. Experiments on classification demonstrate that the descriptor outperforms existing methods on the UIUC as well as the UMD high-resolution dataset.

A main challenge for texture analysis is to construct a compact texture descriptor which is not only highly discriminative to intra-class textures, but also robust to inter-class variations, geometric and photometric changes. In this paper, a new texture descriptor is developed by integrating the local affine-invariant texture features and the global viewpoint-invariant statistics. Based on the pixel clustering using two state-ofart robust local texture descriptors (i.e. SIFT and SPIN), the proposed texture descriptor enables impressive invariance to a wide range of environmental changes (e.g. view changes, illumination changes, surface distortions) by characterizing the spatial distribution of pixel sets using multi-fractal analysis. Experiments on some real datasets (publicly available) showed that the proposed texture descriptor achieved better performance than some state-of-art techniques in texture retrieval and texture classification while the computation cost is significantly reduced.