Variational Bayesian Image Restoration With a Product of Spatially Weighted Total Variation Image Priors

Abstract

Abstract-In this paper a new image prior is introduced and used in image restoration. This prior is based on products of spatially weighted Total Variations (TV). These spatial weights provide this prior with the flexibility to better capture local image features than previous TV based priors. Bayesian inference is used for image restoration with this prior via the variational approximation. The proposed restoration algorithm is fully automatic in the sense that all necessary parameters are estimated from the data and is faster than previous similar algorithms. Numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state-of-the-art restoration algorithms.

A robust iterative algorithm for image restoration

“…These images are the subjects of a recent extensive investigation by an iterative decoupled deblurring BM3D algorithm (IDD-BM3D) [6], which is formulated based on the Nash equilibrium balance of two objective functions undertaking separate denoising and deblurring operations. IDD-BM3D has showed state of the art restoration performance compared to seven other existing methods, which include Fourier-Wavelet regularized deconvolution (ForWaRD) [15], space-variant Gaussian scale mixtures (SV-GCM) [16], shape-adaptive discrete cosine transform(SA-DCT) [17], BM3D deblurring (BM3DDEB) [3], analysis-based sparsity (L0-Abs) [18], adaptive total variation image deblurring by a majorization minimization approach (TVMM) [19], and finally a method based on spatially weighted total variation (CGMK) [20]. We test on the same six scenarios in [6], which have different PSF shapes and blurring strengths as well as noise levels listed in Table 1.…”

Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization

“…One can see that there are many noise residuals and artifacts around edges in the deblurred images by the iterated wavelet shrinkage method [10]. The TV-based methods in [42] and [45] are effective in suppressing the noises; however, they produce over-smoothed results and eliminate much image details. The l 0 -norm sparsity based method of [46] is very effective in reconstructing smooth image areas; however, it fails to reconstruct fine image edges.…”

“…Additive Gaussian white noises with standard deviations 2 and 2 were then added to the blurred images, respectively. We compare the proposed methods with five recently proposed image deblurring methods: the iterated wavelet shrinkage method [10], the constrained TV deblurring method [42], the spatially weighted TV deblurring method [45], the l 0 -norm sparsity based deblurring method [46], and the BM3D deblurring method [58]. In the proposed ASDS-AReg Algorithm 1, we empirically set γ = 0.0775, η = 0.1414, and τ i,j =λ i,j /4.7, where λ i,j is adaptively computed by Eq.…”

A Two-Stage Method for Piecewise-Constant Solution for Fredholm Integral Equations of the First Kind

“…The Tikhonov regularization method [9], the truncated singular value decomposition (TSVD) method [10], the modified TSVD (MTSVD) method [11], the Chebyshev interpolation method [12], the collocation method [13,14], the projected Tikhonov regularization method [15], and so on, are applied to obtain approximate continuous solutions of Equation (2). The total variation (TV) regularization method [16][17][18][19][20][21][22], adaptive TV methods [23][24][25][26][27], the piecewise-polynomial TSVD (PP-TSVD) method [28], and so on, are applied to obtain approximate piecewise-continuous solutions.…”