Images compressive sensing reconstruction by inpainting

During the last years, compressive sensing by random sampling has received a growing attention due to positive theoretical and experimental results. However, the algorithms used for reconstruction, generally based on L1 norm minimization, are very complex and time consuming. The major effect of random sampling is the appearance of missing pixels. Because inpainting algorithms are able to fill the missing data, we propose to use them as CS reconstruction algorithms. For the case of CS images obtained by random sampling, we propose the inpaint_nans algorithm for reconstruction. We justify our proposal by simulation results and comparisons with L1 norm based CS reconstruction algorithms.