Abstract
This paper studies a new convex variational model for denoising and deblurring images with multiplicative noise. Considering the statistical property of the multiplicative noise following Nakagami distribution, the denoising model consists of a data fidelity term, a quadratic penalty term, and a total variation regularization term. Here, the quadratic penalty term is mainly designed to guarantee the model to be strictly convex under a mild condition. Furthermore, the model is extended for the simultaneous denoising and deblurring case by introducing a blurring operator. We also study some mathematical properties of the proposed model. In addition, the model is solved by applying the primal-dual algorithm. The experimental results show that the proposed method is promising in restoring (blurred) images with multiplicative noise.
Highlights
Image restoration problems [1,2,3,4,5,6,7,8,9] have attracted a great amount of attention in real applications
Based on the works [11, 36, 39], we investigate a new convex variational model in this paper, where the image amplitude is considered, and the fidelity term is deduced from the probability density function of the Nakagami distribution and a quadratic penalty term is derived from the statistical property of Nakagami distribution, which guarantees the proposed model to be strictly convex under a mild condition. e convex model guarantees the uniqueness of the solution
We compare our method in the denoising case with the Lee filters [20], the speckle reducing anisotropic diffusion (SRAD) method [45], the probabilistic patch-based (PPB) method [27], and the model (13) with α 0 using the algorithm adopted in [39], while in the deblurring and denoising case, our method is compared with the AA-like method
Summary
Image restoration problems [1,2,3,4,5,6,7,8,9] have attracted a great amount of attention in real applications. The image to be recovered is assumed to be degraded by multiplicative gamma noise Based on this assumption, a series of variational models, including the ZWM model [29], the AA model, and its variants and convexity improvements (e.g., the exponent-based models [30,31,32,33], the mV model [34], the TwL-mV model [35], and DZ model [36]), are proposed, where the regularization terms generally play a key role to preserve the image structure such as edge detail. We arrange some numerical comparisons on simulated images and real SAR images to illustrate the efficiency of the model
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