A general framework for soft-shrinkage with applications to blind deconvolution and wavelet denoising

We consider the abstract problem of approximating a function ψ0∈L1(Rd)∩L2(Rd) given only noisy data ψδ∈L2(Rd). We recall that minimization of the corresponding Tikhonov functional leads to continuous soft-shrinkage and prove convergence results. If the noise-free data ψ0 belongs to the source space L1−u(Rd)∩L2(Rd) for some 0