High order statistics based blind deconvolution of bi-level images with unknown intensity values

Abstract

We propose a novel linear blind deconvolution method for bi-level images. The proposed method seeks an optimal point spread function and two parameters that maximize a high order statistics based objective function. Unlike existing minimum entropy deconvolution and least squares minimization methods, the proposed method requires neither unrealistic assumption that the pixel values of a bi-level image are independently identically distributed samples of a random variable nor tuning of regularization parameters.We demonstrate the effectiveness of the proposed method in simulations and experiments.

Geometric and Visual Reconstruction of Binary Shapes

“…The deconvolution of binary images like document images has been addressed by several researchers (see [51], [55], [59] and [95]). In most of these algorithms, the problem is traced back the to the solution of a system of equations which then solved by some iterative optimization technique.…”

“…For binary deconvolution such measures are used to prescribe binary values for the solutions in [115] and [58]. In [51], Kim et al proposed a blind deconvolution method for binary images with unknown intensity levels. The objective functional included a discretization term (a normalized kurtosis statistics) which enforces binary solutions.…”

“…In this chapter, we introduce a a binary tomography reconstruction method which applies the same higher order statistics based discretization term described in [51]. In our method, the weight of this term is increased during the optimization process to gradually enforce binary solutions which results in a graduated non-convexity optimization scheme [17].…”

“…Obviously, the value of this mid-level is initially unknown. In the case of a binary image deconvolution method it was proposed [51], to optimize the value of the mid-level along with the solution and the point-spread-function in the same gradient descent based optimization process. However, we found that in the case of our method it is more efficient to estimate the mid-level directly to each intermediate solutionx based on the analysis of the discretization function.…”