We propose variational models for image inpainting in wavelet domain, which aims to filling in missing or damaged wavelet coefficients in image reconstruction. The problem is motaviated by error concealment in image processing and communications. It is closely related to classical image inpainting, with the difference being that the inpainting regions are in the wavelet domain. This brings new challenges to the reconstructions. The new variational models, especially total variation minimization in conjunction with wavelets lead to PDE's,in the wavelet domain and can be solved numerically. The proposed models have effective and automatic control over geometric features of the inpainted images including sharp edges, even in the presence of substantial loss of wavelet coefficients, including in the low frequencies. This work is joint with Tony Chan (UCLA) and Jackie Shen (Minnesota).