Abstract In the framework of sparse decomposition, an image deconvolution functional variation model in the Besov smooth space is proposed. The data item is constrained in the negative Hilbert-Sobolev space, while the regularization item is constrained by sparsity and smoothness. Both the sparsity and the smoothness are taken into account by regarding the L1 norm of the redundant dictionary as a sparsity measure and semi-norm as image smoothness measure in Besov space. The operator splitting method is adopted due to the difficulty in solving this mode directly. The original model is split into two parts: image deconvolution and sparse decomposition. Thus, it is solved using cross-iterative method. The resolution of the model pseudo-code is given in detail and the convergence of the algorithm is verified experimentally. The results show that deconvolution model is better than other models.
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2012, Vol. 25 
