A convex regularization model for image restoration

• A second-order convex combination filter is proposed for speckled images.
• The model restores images from multiplicative data-dependent noise.
• The filter switches between its linear and nonlinear behaviors.
• The switching is controlled by the underlying image features.
• This conditional switching considerably reduces the staircase effects.

Many variational formulations are introduced over the last few years to handle multiplicative data-dependent noise. Some of these models seek to minimize the Total Variation (TV) norm of the absolute gradient function subject to given constraints. Since the TV-norm (well-defined in the space of bounded variations (BVs)) minimization eventually results in the formation of piece-wise constant patches during the evolution process, the filtered output appears blocky . In this work the block effect (commonly known as staircase effect) is being handled by using a convex combination of TV and Tikhonov filters, which are defined in BV and L2L2 (square-integrable functions) spaces, respectively. The constraint for the minimizing functional is derived based on a maximum a posteriori (MAP) regularization approach, duly considering the noise distributions. Therefore, this model is capable of denoising speckled images, whose intensity is Gamma distributed. The results are demonstrated both in terms of visual and quantitative measures.

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