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Compressive Sensing Deconvolution (CS Deconvolution) is a new challenge problem encountered in a wide variety of image processing fields. A compound variational regularization model which combined total variation and curve let-based sparsity prior is proposed to recovery blurred image from compressive measurements. We propose a novel fast algorithm using variable-splitting and Dual Douglas-Rachford operator splitting methods. Experiments demonstrate our proposed algorithm can obtain high-resolution data from highly incomplete measurements.