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On the solvability in Sobolev spaces and related regularity results for a variant of the TV-image recovery model: the vector-valued case. (English) Zbl 1382.49044
Summary: We study classes of variational problems with energy densities of linear growth acting on vector-valued functions. Our energies are strictly convex variants of the TV-regularization model introduced by L. I. Rudin et al. [Physica D 60, No. 1–4, 259–268 (1992; Zbl 0780.49028)] as a powerful tool in the field of image recovery. In contrast to our previous work we here try to figure out conditions under which we can solve these variational problems in classical spaces, e.g. in the Sobolev class \(W^{1,1}\).

MSC:
49N60 Regularity of solutions in optimal control
62H35 Image analysis in multivariate analysis
49K27 Optimality conditions for problems in abstract spaces
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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