Abstract. Image restoration is critical across many fields, as it addresses the challenge of recovering clear images from degraded data. Two prominent approaches to this problem are wavelet-based methods and partial differential equation (PDE) models. Wavelet methods can be viewed as discrete analogs of PDE models, and through asymptotic analysis, wavelet models often converge to PDE-based approaches such as the total variation model. Wavelet methods are known for their simple implementation and multiscale time-frequency analysis, while PDE models provide a geometric interpretation of image structures, particularly edges. The relationship between these two approaches offers a comprehensive framework for image restoration. This paper designs a wavelet frame-based image restoration model, focusing on enhancing edge preservation and regularity. More importantly, we establish a connection to the [Formula: see text] version of the Mumford–Shah model, showing that the wavelet model converges to this variational model. This connection is significant, as it combines the geometric explanation of edges in the Mumford–Shah model with the simplicity of wavelet-based implementation. The primary contribution of this paper lies in the asymptotic analysis and proof of convergence of the two-scale wavelet model to the [Formula: see text] Mumford–Shah model, providing both theoretical insights and practical wavelet models for image restoration with enhanced edge detection.

Clustering Web 2.0 items (i.e., web resources like videos, images) into semantic groups benefits many applications, such as organizing items, generating meaningful tags and improving web search. In this paper, we systematically investigate how user-generated comments can be used to improve the clustering of Web 2.0 items. In our preliminary study of Last.fm, we find that the two data sources extracted from user comments -- the textual comments and the commenting users -- provide complementary evidence to the items' intrinsic features. These sources have varying levels of quality, but we importantly we find that incorporating all three sources improves clustering. To accommodate such quality imbalance, we invoke multi-view clustering, in which each data source represents a view, aiming to best leverage the utility of different views.