3D inpainting using sparse representations
Résumé
During data acquisition, the loss of data is usual. It can be due to malfunctioning sensors of a CCD camera or any other acquiring system, or because we can only observe a part of the system we want to analyze. This problem has been addressed using diffusion through the use of partial differential equations in 2D and in 3D, and recently using sparse representations in 2D in a process called inpainting which uses sparsity to get a solution (in the masked/unknown part) which is statistically similar to the known data, in the sense of the transformations used, so that one cannot tell the inpainted part from the real one. It can be applied on any kind of 3D data, whether it is 3D spatial data, 2D and time (video) or 2D and wavelength (multi-spectral imaging). We present inpainting results on 3D data using sparse representations. These representations may include the wavetet transforms, the discrete cosine transform, and 3D curvelet transforms.