Abstract
The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines the overlapping group sparse (OGS) total variation with the high-order nonconvex total variation, can alleviate the staircase artifacts while preserving the original sharp edges. We use the framework of the alternating direction method of multipliers to design an efficient minimization algorithm for the proposed model. Since the objective function is the sum of the non-quadratic log-likelihood and nonconvex nondifferentiable regularizer, we propose to solve the intractable subproblems by the majorization-minimization (MM) method and the iteratively reweighted least squares (IRLS) algorithm, respectively. Numerical experiments show the efficiency of the proposed method for Poissonian image restoration including denoising and deblurring.
Highlights
In many real applications, during the image recording, the measurement of light inevitably leads to the uncertainty of striking particles on the image sensor
We quantitatively evaluate the performances of the proposed method and the competing methods by means of the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM), defined as log nMAXf kf À ^f k2
HTVp-overlapping group sparse (OGS) 31.17/0.91 34.95/0.93 36.43/0.95 30.97/0.91 34.62/0.92 36.18/0.94 30.31/0.89 33.90/0.92 35.22/0.94 29.20/0.87 32.55/0.90 34.18/0.93 In Fig 4, we show the degraded “dolphin” images which are blurred by the corresponding kernels and further corrupted by the Poisson noise of noise level 200, as well as its restored versions obtained through our method and the competitive methods
Summary
In many real applications, during the image recording, the measurement of light inevitably leads to the uncertainty of striking particles on the image sensor. In addition to the methods mentioned above, other authors employed the effective optimization techniques for solving the TV regularized Poisson deblurring model, including the alternating extra-gradient method [22], the primal-dual method [23, 24] and the alternating direction method of multipliers (ADMM) [25, 26] It is well-known that the TV regularization methods could preserve fine details such as sharp edges, but they often exhibit false jump discontinuities causing spurious staircase artifacts in smooth regions of the restored images.
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