Research On The Application Of Variational Model For The Image Denosing

Digital images paly a very important role in the human perception, which is an important entity for recording, transmission and storage. The digital images are widely used in various fields, such as geological exploration, defense security, agriculture, forestry, science and so on. However, images are often influenced by some of the noise during the process of acquisition, transmission and storage. Thus, the denoising technique for the image is as an importance front-end technology to ensure that people can understand the inherent information, which is to help people to get more accurate and effective information from the image.A denoisng method is to restore corrupted image to what it should look like, which is based on the image degradation model and the prior information of the image itself. The variation model is an effective way to restore noisy image, the expression about the prior information is very important for recovering a noisy image. Some important characteristics of the image described in the form of convex constraints are applied to construct a variation denoising model. Meanwhile, with the rapid development of solving algorithms for variation model in recent years, which provide strong support for the research in the variation model. In this paper, we will based on the characteristics about the piecewise smoothness, the sparsity of the transform coefficients, the sparsity of the over-complete dictionary coefficient, the low rank of image. The restoration of the nature images and hyperspectral images will be studies in detail, the main work and innovations are as follows:1. The restoration of image corrupted by additive Gaussian noise has been studied. The classic total variation (TV) method still have some drawbacks. First, the textures and edges tend to be overly smooth. Secondly, the flat areas are approximated by a piecewise constant surface resulting in a staircasing effect. Thirdly, a compromise between regularity on the flat areas and preservation of textures is based on the choice of the trade-off parameter, while the parameter is difficult and image dependent to choose. We will introduce an adaptively weighted four-directional total variation (Ada-4WTV) method is introduced to improve the classic TV method. The adaptive trade-off parameter is set for every pixel. On the flat areas, the restored solution is close to the one given by NL-means, while the pixels around singular structures and textures, the restored image tends to the solution by the TV method. Also four weights are then designed to prevent the textures and edges from overly smoothed and mistaking the textures as noise. Furthermore, the fast gradient projection (FGP) algorithm is extended to implement the Ada-4WTV. The experimental results indicate that the Ada-4WTV method adapts to different noise levels and has better performance on keeping the image textures and edges.2. The restoration of hyperspectral image contaminated by mixed noise has been studied. Hyperspectral images (HSIs) are often corrupted by additive zero-mean Gaussian noise plus random-valued impulse noise, the mixed noise makes the restoring problem more difficult. Firstly, the representation of hyperspectral images in over-complete dictionary is sparse. Due to the adverse effects of the impulse noise, we have to classify the two types of noise for training an adaptive over-complete dictionary better. The low-rank property of a clean HSI is explored, the low-rank part is also as a pretreatment result of the hyperspectral image. We calculation the absolute difference between the preprocessed image and the observed image, and then develop a novel noise classifier to identify different noise in the corrupted HSI. Then, an adaptive overcomplete dictionary is trained for HSI patches with the help of an extended K-SVD algorithm. Lastly, we construct a variational model which contains an optional data-fidelity term according to the kind of the image noise and two smooth regularization terms involved in the sparse representation and the low-rank property. The fixed variable iterative optimization algorithm to minimize the constructed variational model. The experimental results obtained on both simulated and real noisy HSIs data validate the effectiveness of the proposed method. The proposed method can simultaneously preserve the original HSI and avoid spectral distortion while removing noise.