Research Of Image Restoration Based On Hessian Matrix Norm Regularization Algorithm

It is very difficult to avoid the blocked structure and decreased sharpness in thefield of digital image for various reasons. However, in practice, the degraded imageswould seriously affect the results of our analysis, so we need clean images. Therefore,image restoration(image deblurring, denoising, etc.) has a very important significance.Image restoration method, recover the low-quality image mentioned previously, and getclear, ideal image, is the basis of image analysis, pattern recognition and other advancedimage processing technology. Image restoration has been widely used in radar images,remote sensing images and other areas.In the history of image restoration development, the classical way is achieved byfiltering methods. As it is well known, most of the information is retained in the edge ofimage. So the desirable method can not only maintain the details of edge and canremove the noise. It is difficult for classical filtering methods to deal with theseproblems caused by the aliasing. The image processing method based on partialdifferential equations and higher order regularization method for solving thiscontradiction in image restoration provides a new approach.The total-variation（TV）functional has gained a great success, since it can producewell-preserved and sharp edges. Moreover, its convexity permits the design of efficientalgorithms. However, it leads to the well-known staircase effect when applied to signalsthat are not necessarily piecewise constant. To attenuate even eliminate the staircaseeffect, there is a growing interest in replacing TV by some higher order differentialoperator. Based on this foundation, we propose a second-order Hessian matrix normregularization method. This method effectively deal with the staircase effect, whilepreserving some of the most favorable properties of TV, such as convexity, homogeneity,rotation and translation invariance.In order to implement this model, we introduce an effective method to minimize theobjective function. The algorithm is based on MM method, and PCG method anditerative weighted least square method are used for accelerating. The numericalexperiments show that this model obtains good results in image restoration, and gets abetter visual effect.