In multi-view learning applications, like multimedia analysis and information retrieval, we often encounter the corrupted view problem in which the data are corrupted by two different types of noises, i.e., the intra- and inter-view noises. The noises may affect these applications that commonly acquire complementary representations from different views. Therefore, how to denoise corrupted views from multi-view data is of great importance for applications that integrate and analyze representations from different views. However, the heterogeneity among multi-view representations brings a significant challenge on denoising corrupted views. To address this challenge, we propose a general framework to jointly denoise corrupted views in this paper. Specifically, aiming at capturing the semantic complementarity and distributional similarity among different views, a novel Heterogeneous Linear Metric Learning (HLML) model with low-rank regularization, leave-one-out validation, and pseudo-metric constraints is proposed. Our method linearly maps multi-view data to a high-dimensional feature-homogeneous space that embeds the complementary information from different views. Furthermore, to remove the intra- and inter-view noises, we present a new Multi-view Semi-supervised Collaborative Denoising (MSCD) method with elementary transformation constraints and gradient energy competition to establish the complementary relationship among the heterogeneous representations. Experimental results demonstrate that our proposed methods are effective and efficient.