Nonlinear anisotropic diffusion methods for image denoising problems: Challenges and future research opportunities

Adaptive Numerical Regularization for Variational Denoising Model with Complementary Approach

“…The other applications are related to the motion of the image like robot vision, optic flow stereo vision etc. In the optic flow one computes the movement of the pixels in a sequence of images [9,13,21]. Denoising of the image is the application which enhances the image by reducing high oscillation in image without any loss of much data and maintains the contours and edges.…”

“…The main discretization method for the solution of the denoising problems in this paper is considered as adaptive finite element method (FEM) [5,6,21]. The mathematical imaging problem is based on the Partial differential equation which is obtained from the optimization of designed energy functional.…”

“…In most of the smoothing methods for inverse problems, the selection of the regularization parameters is proposed as uniform over the whole domain of the computation [3-5, 7, 11, 21]. The choice of the smoothing parameter in an adaptive way and specifically their choice as a scalar function over the given domain of the computation is an interesting idea of the computation [2,7,14,[21][22][23].…”

“…It has been observed in the literature that the ill-posed inverse problems arising in the Science and engineering generally solved by the regularization methods These strategies play an effective role in the solution of many ill-posed inverse problems but due to their non-linear nature many complexities may arise in the solution strategies, therefore practitioners look forward to the linear approaches with modern and novel smoothing techniques [9]. Such strategies have been successfully applied in the image sciences where the famous applications are image denoising [2,3,3,6,11,18,[21][22][23], optical flow problems [9,10,13] and stereo vision problems [21] . The Partial Differential Equation (PDEs) based approaches have been extensively used in image processing due to their modeling flexibility and numerical implementations [3,6,9,13,18,22,25].…”

“…Various settings of the data term and smoothness term for Eq. ( 2) have been proposed in the literature [7,18,21]. Keeping in view the model (2) and over-all work on the PDE's based regularization it is observed that no one is still very confident to say that the major diffusion role is played in model ( 2) by the smoothing term or by the data term [9,13], however there is ambiguity that these terms may contradict each other.…”