Research On Color Image Denoising Using Higher-order PDE

Digital images are corrupted during acquisition and transmission.The presence of noise destroys the real information of the original image,and makes it difficult for the following higher-level process.Being the important attribute of color images,color can simplify the feature extraction and recognition.So color image denoising is the prime task of image processing.This task is complicated,as there are many kinds of noise,and its distribution is random.The aim of denoising is to suppress noise while protecting details and edges as much as possible.PDE(Partial differential equation)is an effective tool to build the denoising model.It uses a priori knowledge of the degradation phenomenon to build a energy functional.Then the image denoising task is converted to a optimization problem.The lower-order PDE can get a piecewise constant image,which suffers the staircasing effect.While the higher-order PDE has a big response to the outlier and tends to smooth the edge.For the color image denoising,it needs to consider how to couple different color channels,and the computational efficiency.There is always a tradeoff between noise suppression and preserving actual image discontinuities,and between efficiency and accuracy.An improved iterating algorithm is proposed to eliminate the speckles preserved by the local curvature-based model as geometrical characteristic.It utilizes the local curvature coupling three channels as the regularizing term,then detects speckles by using local statistics values.The relaxed median filter is introduced to suppress these speckles.This algorithm can accelerate the progress of evolution and eliminate the speckles while protecting the image structure information.A geometry driven higher-order model for removing noise from color images is proposed to eliminate the staircasing effect that accompanies the use of first-order derivatives.This novel method introduces a weighted function to improve the edge preserving ability.Analyzing and generalizing related models that use the first-order derivative to measure the oscillations in an image under the Riemann geometry framework,we generate a second-order derivative matrix.Based on its Frobenius norm,we construct a higher-order variational model and get a partial differential equation.In order to preserve edges during the diffusion process,the new multichannel coupling nonlinear model uses the gradient information to guide the higher-order diffusion.The proposed model consider the relations between single and multiple channels,lower and higher orders,and so on.So it can suppress the noise while eliminating the staircasing effect and giving a better performance at the edge of the color image.Two iterative guided filtering combined with total variation algorithms,called LGTV and CGVTV,are proposed to improve the performance of the guided filter and eliminate the staircasing effect.The input image remains unchanged during the iterations.The iterations consist of two stages.LGTV use the luminance channel of opponent color space to guide itself.Then the result which is smoothed by TV is used as the new guidance image to guide the input image.CGVTV use the color input as the initial guidance image to guide each channel respectively.The guidance image is then updated by the vectorial total variation whose input is the result of the guided filtering.As the quality of the guidance image increase,the performance of the guided filtering is improved.