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Over the past decade, wavelet frames have been widely investigated in the field of image restoration. The success of them is largely attributed to their ability of sparsely representing piecewise smooth functions such as natural images. Classical wavelet frame models mostly are based on the sparsity prior of frame coefficients, e.g., the \(\ell _1\) norm or \(\ell _0\) “norm” regularizer term is commonly employed. The sparsity-promoting regularization has became so prevailing that it is desirable to explore more prior knowledge of the underlying image to achieve better recovery performance, besides the conventional sparsity prior. In this paper, we formulate a new wavelet frame-based truncated \(\ell _0\)–\(\ell _2\) model which simultaneously combines sparsity, nonlocal and support prior of the frame coefficients. Specifically, we focus on investigating the role of these priors play in the regularization model for image restoration problems. Extensive deblurring and denoising experiments are reported to demonstrate the effectiveness of our proposed method, not only in terms of objective PSNR and SSIM improvements over the state-of-the-art algorithms, but also subjectively producing more pleasing recovery output.

Wavelet frame-based image restoration using sparsity, nonlocal, and support prior of frame coefficients