Graph-Based Blind Image Deblurring From a Single Photograph

Abstract

Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel, deconvolve blurry input to restore the target image. In this paper, we propose a graph-based blind image deblurring algorithm by interpreting an image patch as a signal on a weighted graph. Specifically, we first argue that a skeleton image-a proxy that retains the strong gradients of the target but smooths out the details-can be used to accurately estimate the blur kernel and has a unique bi-modal edge weight distribution. Then, we design a reweighted graph total variation (RGTV) prior that can efficiently promote a bi-modal edge weight distribution given a blurry patch. Further, to analyze RGTV in the graph frequency domain, we introduce a new weight function to represent RGTV as a graph l1-Laplacian regularizer. This leads to a graph spectral filtering interpretation of the prior with desirable properties, including robustness to noise and blur, strong piecewise smooth (PWS) filtering and sharpness promotion. Minimizing a blind image deblurring objective with RGTV results in a non-convex non-differentiable optimization problem. We leverage the new graph spectral interpretation for RGTV to design an efficient algorithm that solves for the skeleton image and the blur kernel alternately. Specifically for Gaussian blur, we propose a further speedup strategy for blind Gaussian deblurring using accelerated graph spectral filtering. Finally, with the computed blur kernel, recent non-blind image deblurring algorithms can be applied to restore the target image. Experimental results demonstrate that our algorithm successfully restores latent sharp images and outperforms state-of-the-art methods quantitatively and qualitatively.

Feature Graph Learning for 3D Point Cloud Denoising

“…In the aforementioned GLR, the graph Laplacian L is fixed, which does not promote reconstruction of the target signal with discontinuities if the corresponding edge weights are not very small. It is thus extended to signal-dependent GLR in [4]- [6] by considering L(z) as a function of the graph signal z.…”

“…where M ∈ R K×K is a positive definite (PD) matrix 3 . As a special case, when M is a diagonal matrix with strictly positive diagonal entries, the definition in (6) defaults to that in [27]. Diagonal M can capture the relative importance of individual features when computing δ i,j , but fails to capture possible cross-correlation among features, and thus is sub-optimal in the general case.…”

Single Image Blind Deblurring Using Multi-Scale Latent Structure Prior

“…Recently, with the fast progress of regularization and optimization theory, many sophisticated image priors [3]- [12] were proposed to handle the single image blind image deblurring problem with general blur kernels, such as the mixture of Gaussians prior that fits the heavy-tailed prior of natural images [3], [4], normalized sparse prior [5], framelet based prior [6], l 0 -norm based priors [7], [8], color line prior [9], dark channel prior [10], low rank prior [11] and graph based prior [12], etc. The priors promote image sharpness and penalize image blurriness, which work as a regularizer in the optimization model guiding the solver to converge to the latent sharp image.…”

“…is the data fidelity term, Ψ 1 (k) and Ψ 2 (x) are the regularizers of blur kernel k and latent sharp image x, respectively. Previous methods, such as [3]- [12], [16], introduced sophisticated image priors, which are usually either non-convex or computationally expensive. To tackle the challenging problem mentioned above, we take advantage of the proposed MSLS prior and introduce an efficient local self-example matching strategy to substitute for complex non-convex regularization of x in sharp image reconstruction.…”

“…Tailored to the MSLS prior, we propose an efficient algorithm to solve the blind image deblurring problem, which is much faster than the aforementioned methods [3]- [12], [16]. The proposed algorithm comprises two phases, i.e., we first preliminarily restore sharp images gradually from the coarsest scale to the finest scale, and then perform a refinement in the finest scale.…”