MCALab a toolbox for Signal and Image Decomposition and Inpainting, Some passing remark on inpainting and missing data.

A new version of the MCALab a toolbox for Signal and Image Decomposition and Inpainting by Jalal Fadili, Jean-Luc Starck, Michael Elad, David Donoho is now available here.

Presentation of the toolbox:

Morphological Component Analysis (MCA) of signals and images is an ambitious and important goal in signal processing; successful methods for MCA have many far-reaching applications in science and technology.

Because MCA is related to solving underdetermined systems of equations it might also be considered, by some, to be problematic or even intractable. Reproducible research is essential to give such a concept a firm scientific foundation and broad base of trusted results. MCALab has been developed to demonstrate key concepts of MCA and make them available to interested researchers and technologists. MCALab is a library of Matlab routines that implement the decomposition and inpainting algorithms that we previously proposed in our papers. The MCALab package provides the research community with open source tools for sparse decomposition and inpainting and is made available for anonymous download over the Internet. It contains a variety of scripts to reproduce the figures in our own articles, as well as other exploratory examples not included in the papers. One can also run the same experiments on one’s own data or tune the parameters by simply modifying the scripts. The MCALab is under continuing development by the authors; who welcome feedback and suggestions for further enhancements, and any contributions by interested researchers.

Requirements: Matlab 6.x and later and WaveLab802 or later. It has been successfully run with Matlab 6.x and 7.x under Unix Solaris/Linux/MacOSX. Can somebody please check it under Windows ?

The connection to Compressed Sensing (not that anything I am writing should be related to CS) is as follows: If one thinks of the mask as being part of a restriction operator on the measurement matrix as used in Compressed Sensing, then MCALab can be seen as a CS reconstruction solver for images. As mentioned earlier here in the context of images ( "When is missing data recoverable?" by Yin Zhang) and here in the context of voice recognition ( Using sparse representations for missing data imputation in noise robust speech recognition by Jort Gemmeke and Bert Cranen) it seems that projecting data that is irregularly sampled using random ensembles on top of a 0-1 mask enables one to produce convincing results. One can also note here a different measurement projection in the context of frequency inpainting ( SparSpec : a new method for fitting multiple sinusoids with irregularly sampled data, Sebastien Bourguignon, Hervé Carfantan and Torsten Böhm). In this last case, diracs and sine functions are maximally incoherent so there is no need for Gaussian ensembles.