Study On MGA-based Image Deniosing Algorithm Using Dependence Of Coefficients

With the development of the computer system and our standard of living, digital multimedia becomes an indispensable part of our life. Taking images as an example, we have astonishing pixel numbers today. In the new images form NASA, there are more than4billions of pixels. By the same time, the image processing chips are more easily influenced by the noise. As one of the most classic image processing technologies, denoising is still very useful.In the field of denoising, we can approximately divide the denoising methods into two classes:based on Space and Transform Domain. On the whole, new methods are more willing to protect the image details and to use more complex ways. Among the Space domain methods, NLM and BM3D have made great success. And in the Transform domain methods, good algorithms like K-SVD spring up. But those image-patch-based methods take very long time in search or training, not appropriate for application.In the Transform domain methods, the most popular tools are Fourier Transform, Wavelet Analysis and Multi-scale Geometric Analysis. Fourier Transform is a classic signal processing tool, using a group of orthogonal&complete trigonometric functions to represent the signal. Fourier can represent the signal into frequency domain but can not make located description. Wavelet can perfectly solve this problem. Wavelet uses basic functions that have local-extremumed energy. So it can represent the signal into both frequency and space domain. Owing to these great advantages, the Wavelet is called’the mathematic microscope’.But in the2D situation, Wavelet has numbers of drawbacks. It can only represent the image into3directions in each scale, and can not effectual approach the edge information. Donoho and other researchers invented ridgelet, curvelet, contourlet and other new MGA models to represent the image in better level. The new MGA models can represent the image information into more directions in each scale. As a result, new MGA methods have longer and narrower basic functions, which can more ideally approximate to the image edge.The MGA-based denoising has always been the researching hotspot. But most of the methods only give the image overall processing or combine with other algorithms. The coefficients are only being processed in every subband. But there are vast of correlation in scale-adjacent or direction-adjacent coefficients. The denoising result will be improved, if the correlation is used. Considering the coefficients as4D matrix, the correlation of scale and direction will be shown as the continuous in scale and direction axis. And they respectively have own style. The scale correlation is shown as the superposition in scale adjacent subbands. The directional correlation is shown as the complementation and continuity in direction axis.The SSNF denoising method based on wavelet makes use of scale correlation. It operates the scale adjacent subbands with point multiply, and uses the correlation matrix to get the threshold matrix. In the chapter4of this thesis, there is a NSCT-based algorithm making use of directional correlation with this train of thought and new ways.In the chapter5, a new image analysis plan is proposed. Firstly, many groups of filer are used to process the image to add the image information with dimensions. When the information is scattered in the new domain, we can cluster the information more accurately. So that the structure can be better represented and the image is analyzed.