Abstract
The denoising and deblurring of Poisson images are opposite inverse problems. Single image deblurring methods are sensitive to image noise. A single noise filter can effectively remove noise in advance, but it also damages blurred information. To simultaneously solve the denoising and deblurring of Poissonian images better, we learn the implicit deep image prior from a single degraded image and use the denoiser as a regularization term to constrain the latent clear image. Combined with the explicit L0 regularization prior of the image, the denoising and deblurring model of the Poisson image is established. Then, the split Bregman iteration strategy is used to optimize the point spread function estimation and latent clear image estimation. The experimental results demonstrate that the proposed method achieves good restoration results on a series of simulated and real blurred images with Poisson noise.
Highlights
Where 〈1, Hx − y log Hx〉 is the data term, 1 represents a vector with all elements equal to 1, x is the latent clear image, which usually ensures that the clear image does not contain negative gray values, H is the point spread function, R(x) is the regularization constraint term of the latent clear image, and K(H) is the regularization constraint term of a point spread function
Image noise can be divided into three categories: additive noise, multiplicative noise, and Poisson noise. e logarithm of the multiplicative noise can be processed as additive noise of Gaussian distribution
Most TV regularization-based restoration models can effectively reduce the noise in flat regions, but large staircase effects are introduced in flat regions, and fine details are not preserved in complex structural regions, which limits the practical application of the TV regularization term
Summary
RED, as a regularization function, is given by the following formula: ρ(x) 1xT[x − f(x)],. Erefore, we use the nonlocal mean denoiser as the regularization term of Poisson image denoising in the proposed method in this paper. To obtain good denoising results while preserving the image details, we introduce equation (6) into the objective function 2 for Poissonian image deblurring and use RED as the denoising regularization term in the Poisson image deblurring model. E existence of the L0 norm in the third term of equation (8) makes the solution somewhat difficult, the split Bregman method is used to introduce auxiliary variable v, and equation (8) is changed to the following equation: min 〈1, d1 ,x,θ,H μ2 d1. Given fixed variables d1, u1, and θ, the point spread function H can be solved by the following formula: H (11).
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