An issue in data analysis is that of incomplete data, for example a photograph with scratches or seismic data collected with fewer than necessary sensors. There exists a unified approach to solving this problem and that of data separation: namely, minimizing the norm of the analysis (rather than synthesis) coefficients with respect to particular frame(s).There have been a number of successful applications of this method recently. Analyzing this method using the concept of clustered sparsity leads to theoretical bounds and results, which will be presented. Furthermore, necessary conditions for the frames to lead to sufficiently good solutions will be shown, and this theoretical framework will be use to show that shearlets are able to inpaint larger gaps than wavelets. Finally, the results of numerical experiments comparing this approach to inpainting to others will be presented.