Graph-signal Reconstruction and Blind Deconvolution for Structured Inputs

Key to successfully deal with complex contemporary datasets is the development of tractable models that account for irregular structure information at hand. This paper provides a comprehensive and unifying view several sampling, reconstruction, recovery problems signals defined on domains can be accurately represented by graph. The workhorse assumption (partially) observed modeled as output graph filter structured (parsimonious) input signal. When either or coefficients are known, this tantamount assuming interest live subspace supporting neither model becomes bilinear. Upon imposing different priors additional coefficients, broad range relevant problem formulations arise. goal then leverage those priors, shift operator graph, samples signal recover: non-sampled nodes (graph-signal interpolation), (deconvolution), (system identification), any combination thereof (blind deconvolution).