IEEE Trans Image Process - Efficient algorithms for robust recovery of images from compressed data.

Tópicos

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Resumo

Compressed sensing (CS) is an important theory for sub-Nyquist sampling and recovery of compressible data. Recently, it has been extended to cope with the case where corruption to the CS data is modeled as impulsive noise. The new formulation, termed as robust CS, combines robust statistics and CS into a single framework to suppress outliers in the CS recovery. To solve the newly formulated robust CS problem, a scheme that iteratively solves a number of CS problems--the solutions from which provably converge to the true robust CS solution--is suggested. This scheme is, however, rather inefficient as it has to use existing CS solvers as a proxy. To overcome limitations with the original robust CS algorithm, we propose in this paper more computationally efficient algorithms by following latest advances in large-scale convex optimization for nonsmooth regularization. Furthermore, we also extend the robust CS formulation to various settings, including additional affine constraints, l1-norm loss function, mix-norm regularization, and multitasking, so as to further improve robust CS and derive simple but effective algorithms to solve these extensions. We demonstrate that the new algorithms provide much better computational advantage over the original robust CS method on the original robust CS formulation, and effectively solve more sophisticated extensions where the original methods simply cannot. We demonstrate the usefulness of the extensions on several imaging tasks.

Resumo Limpo

compress sens cs import theori subnyquist sampl recoveri compress data recent extend cope case corrupt cs data model impuls nois new formul term robust cs combin robust statist cs singl framework suppress outlier cs recoveri solv newli formul robust cs problem scheme iter solv number cs problemsth solut provabl converg true robust cs solutioni suggest scheme howev rather ineffici use exist cs solver proxi overcom limit origin robust cs algorithm propos paper comput effici algorithm follow latest advanc largescal convex optim nonsmooth regular furthermor also extend robust cs formul various set includ addit affin constraint lnorm loss function mixnorm regular multitask improv robust cs deriv simpl effect algorithm solv extens demonstr new algorithm provid much better comput advantag origin robust cs method origin robust cs formul effect solv sophist extens origin method simpli demonstr use extens sever imag task

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