Abstract
A new Plug-and-Play (PnP) alternating direction of multipliers (ADMM) scheme is proposed in this paper, by embedding a recently introduced adaptive denoiser using the Schroedinger equation's solutions of quantum physics. The potential of the proposed model is studied for Poisson image deconvolution, which is a common problem occurring in number of imaging applications, such as limited photon acquisition or X-ray computed tomography. Numerical results show the efficiency and good adaptability of the proposed scheme compared to recent state-of-the-art techniques, for both high and low signal-to-noise ratio scenarios. This performance gain regardless of the amount of noise affecting the observations is explained by the flexibility of the embedded quantum denoiser constructed without anticipating any prior statistics about the noise, which is one of the main advantages of this method. The main novelty of this work resided in the integration of a modified quantum denoiser into the PnP-ADMM framework and the numerical proof of convergence of the resulting algorithm.
Highlights
R ESTORATION of a distorted image is one of the most fundamental tasks in inverse problems related to imaging applications such as denoising, deblurring, superresolution, compression or compressed sensing
The nonuniform nature of the convolution operator under a variance stabilizing transformation (VST) leads to fundamental flaws in the deconvolution algorithms [31], [32], [61]. We address these shortcomings by embedding into a PnP-alternating direction method of multipliers (ADMM) scheme a new adaptive denoiser [62], [63] designed by borrowing tools from quantum mechanics
Gaussian denoiser-based PnP-ADMM algorithms have achieved enormous success in this domain of image restoration, they are still facing a theoretical limitation related to the Anscombe transformation used to approximately transform the Poisson noise into additive Gaussian noise
Summary
R ESTORATION of a distorted image is one of the most fundamental tasks in inverse problems related to imaging applications such as denoising, deblurring, superresolution, compression or compressed sensing. In number of applications such as limited photon acquisition, X-ray computed tomography, positron emission tomography, etc., the noise degrading the acquired data follows a Poisson distribution These Poissonian models have been extensively studied in the fields of astronomical [1]–[3], photographic [4], [5] or biomedical [6]–[11] imaging. The inversion process is expressed as the estimation of a clean image x ∈ Rn from observed degraded image y ∈ Rm. The estimation of the underlying hidden image from this distorted observation is often formulated as the optimization of a cost function implementing the idea of the maximum a posteriori (MAP) estimator [12], i.e., the maximization of the posterior probability, defined as x = arg max P (x|y), (1). ADMM is an iterative convex optimization algorithm, resulting from the fusion of the dual decomposition method with the method of multipliers [65]–[70].
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