Total Variation Based Image Decompression

With the continuous expansion of Internet information applications,the image pro-cessing has been an important application technology in the fields of computer vision.In order to reduce the storage space of the image and the transmission time,we need to the eliminate data redundancy between the pixels to compress the image.Therefore,image compression is an important research direction in digital image processing.JPEG is a kind of transform code,which has become a widely used compression standard for still images.Its biggest advantage is that it can choose the compression ratio freely according to the needs of the users and make the decision between the image quality and the cost.But the quantization and rounding operations resulting in data loss in compression side,so that the JPEG decompression images appear some block effects and obvious compression artifacts.MPEG compression standard is a video compression method,which is mainly used for video data storage,broadcast television and video streaming network trans-mission.MPEG removes intra-frame redundancy similar to JPEG for still images.M-PEG videos can achieve high compression ratio,reduce the videos storage space and the transmission time.But the high compression ratio also means that the loss of data,results in poor quality of decoded videos with significant compression artifacts.In this thesis,with the still image and video as the research objects,we use the total variation models to decode the JPEG and MPEG compressed images,and develop the optimal numerical algorithms,so as to reduce the compression artifacts of the decoded images.The main work in this paper is as follows:(1)We briefly disccuss the reasons of the compression traces in JPEG and MPEG decoding images,and summarize the research status of eliminating the quantization noise of image compression.(2)We introduce the standard JPEG coding algorithm.In order to facilitate the modeling,we construct the mathematic model of JPEG coding,and obtain a priori con-dition of the original images according to the quantization interval of DCT coefficients.We discuss the basic theory of 2-dimensional total variational method,and construc-t a optimization model based on total variation to eliminate quantization noise.We take advantage of primal-dual method to solve the model so that we obtain the total variational JPEG decoding images.(3)We introduce the standard MPEG video coding algorithm,and obtain a quan-tization interval according to the quantization rounding.We discuss the basic theory of the total variational method about 3-D videos,and we Respectively construct the total variational model of coupling and segregating time dimension.The two kinds of total variational models are transformed into the minimax problem,and we use primal-dual method to solve the two models so that we get two post-processing MPEG videos.