Regularized supervised Bayesian approach for image deconvolution with regularization parameter estimation

Bouchra Laaziri,Said Raghay,Abdelilah Hakim

doi:10.1186/s13634-020-00671-w

Bouchra Laaziri, Said Raghay + Show 1 more

Open Access

https://doi.org/10.1186/s13634-020-00671-w

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Abstract

Image deconvolution consists in restoring a blurred and noisy image knowing its point spread function (PSF). This inverse problem is ill-posed and needs prior information to obtain a satisfactory solution. Bayesian inference approach with appropriate prior on the image, in particular with a Gaussian prior, has been used successfully. Supervised Bayesian approach with maximum a posteriori (MAP) estimation, a method that has been considered recently, is unstable and suffers from serious ringing artifacts in many applications. To overcome these drawbacks, we propose a regularized version where we minimize an energy functional combined by the mean square error with H1 regularization term, and we consider the generalized cross validation (GCV) method, a widely used and very successful predictive approach, for choosing the smoothing parameter. Theoretically, we study the convergence behavior of the method and we give numerical tests to show its effectiveness.

Highlights

Images are indispensable in science and everyday life
We propose a regularized maximum a posteriori (MAP) method where we minimize an energy functional combined by the mean square error with H1 regularization term: arg min g − Hf
3 Results and discussion This section presents a culmination of all the numerical tests we performed of the proposed approach for solving image deconvolution problem, and compares it with the Wiener filter, the Richardson-Lucy deconvolution [30], the total variation (TV) approach, and the bilateral TV (BTV) method

Summary

Introduction

Images are indispensable in science and everyday life. Images are obtained in areas ranging from everyday photography to astronomy, medical imaging, remote sensing, and microscopy. There is an underlying object we wish to observe, which is the original or true image. This true image is the ideal representation of the observed scene. The observation process is never ideal: there is uncertainty in the measurements, such as blur, noise, and other types of degradation. Image restoration aims to recover an estimate of the true image from the degraded observations. The key to being able to solve this problem is proper incorporation of prior knowledge about the original image into the restoration process

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Results

Conclusion