Performance Bounds for Cosparse Multichannel Signal Recovery via Collaborative-TV
We consider a new class of regularizers called collaborative total variation (CTV) to cope with the ill-posed nature of multichannel image reconstruction. We recast our reconstruction problem in the analysis framework from compressed sensing. This allows us to derive theoretical measurement bounds that guarantee successful recovery of multichannel signals via CTV regularization. We derive new measurement bounds for two types of CTV from Gaussian measurements. These bounds are proved for multichannel signals of one and two dimensions. We compare them to empirical phase transitions of one-dimensional signals and obtain a good agreement especially when the sparsity of the analysis representation is not very small.
KeywordsGaussian Measurement Measurement Bound Gaussian Width Gaussian Random Matrix Finite Difference Operator