Research On Signal And Image Processing Algorithms Based On Non-Local Information And Their Applications

In signal and image processing field, the most crucial and also the most challenging issue is to find an effective way to represent signals or images. Traditionally, some function models or probability models are usually constructed based on certain assumptions for the signal or image as their representations. However, the complexity and variety of the signal and image make it a very difficult task to construct such a parametric model, which requires much prior knowledge about the signal. And what's more, the model only works well for some specific signals or images under the assumption constraints.When people are still trying their best to find a more general parametric model to well represent signals, both the requirements for dealing with mass of data and the performance improvement of computers give birth to a new kind of signal and image analysis and processing methods-data driven methods, also known as example-based methods. Different with the traditional model-based methods, this new technology represents a signal based on the information provided by the data itself, and it is very suitable and effective for dealing with those data which are difficult to model due to their complexity.Every pixel in an image is not alone; it builds up geometric structures together with its surrounding neighbors. A square window centered at a pixel, also called a patch, can well reflect its structure property. And all the patches corresponding to each pixel can constitute a set or a space, which can act as an overcomplete representation of an image. Meanwhile, self-similarity is an essential property of an image, i.e., the pixels at different locations resemble with each other. For example, the pixels along a long edge, or more specifically, the pixels in the texture images or images with periodic patterns all show strong long-range correlations. In example-based algorithms, the non-local similarity information provided by an image itself can be made use of to tackle some image processing problems. Currently, the algorithms based on non-local patch similarity have found their applications in many fields, such as texture synthesis, image and video denoising, image super-resolution etc., and have shown their superiority.In this work, with signal blocks and image patches as the basic representations for a signal or an image, the algorithms and their applications based on non-local similarity information for texture synthesis and signal and image denoising are studied systematically. The main contributions of this thesis include:(1) A fast texture synthesis algorithm based on DWT is proposed.A fast texture synthesis algorithm based on DWT is proposed to improve the efficiency of the pixel-domain image quilting algorithm. The quilting of the coefficients is carried out only in the approximation sub-band, and then the coefficients in all detail sub-bands are synthesized simultaneously based on the parent-child relationship of the coefficients within the same scale and across different scales. On one hand, due to the reduced size of the low resolution image, larger texture pattern characteristics can be captured just by smaller sized patches; in addition, the number of pixels both for similarity comparison and to be synthesized become smaller, so the computational complexity is greatly reduced. On the other hand, the texture characteristics can be better represented in the wavelet domain, the coefficients in different sub-bands can give their contributions to the similarity comparison, which can help to generate visually more appealing textures. The synthesis results show that the proposed approach can synthesize a wide range of textures, and it is more efficient than the original one.(2) A modified similarity metric for the non-local means algorithm is proposed.In the original non-local means algorithm, only translational neighborhood patterns are used in similarity comparison, which do not fully exploit the symmetric characteristics that exist in many images. To address this problem, the isometry transformations in fractal theory are introduced to modify its similarity metric, so that the self-similarity property of images can be better made use of. In this way, the similarity comparisons become more accurate and more candidate pixels can be picked out for averaging a pixel to be restored, and the larger number of candidate pixels can provide a better precondition for non-local means denoising.(3) An adaptive filtering parameter selection method is put forward.The filtering parameter plays an important role in the non-local means algorithm, which takes a fixed value empirically for the whole image in the original scheme. Generally speaking, different pixels own different properties, the fixed global parameter will result in over-smoothing some pixels while not being able to filter others sufficiently. And what's more, when the noise level exceeds a certain value, it is no longer possible to choose a global parameter such that the noise is removed everywhere without destroying structures somewhere else in the image. It is noted that the ratio of the Euclidean distance between neighborhoods and the filtering parameter determines the weight. For different pixels in an image, the Euclidean distances between neighborhoods in the search region satisfy different distributions, so better denoising results should be obtained by choosing different filtering parameters for different pixels. Motivated by this idea, an adaptive filtering parameter selection method based on image intensity statistics is proposed, which can determine the filtering parameter adaptively according to individual pixel property. Experiment results verify the effectiveness of the proposed method.(4) A two-stage non-local means filtering strategy is proposed.The neighborhood similarity is measured by Euclidean distances between neighborhood gray value vectors in the non-local means algorithm. The calculation of the Euclidean distance will be affected by noise, especially when the noise level is too high, the Euclidean distances obtained on noisy images can no longer well reflect the neighborhood similarity. To solve this problem, a two-stage non-local means filtering strategy is proposed. With some noise removed with a smaller filtering parameter in the first stage, the similarity can be obtained more accurately and better adapted to the non-local means algorithm in the second filtering stage. Experiment results demonstrate that compared with the original algorithm, more noise can be removed by the proposed two-stage filtering approach, and it performs even better under higher noise level cases.(5) An adaptive search based non-local means filtering scheme is proposed.The non-local means algorithm uses the weighted average of all pixels in an image to recover a noise-free pixel. However, if the pixel values used for average do not lie in the same gray levels as the one to be restored, they will make negative contributions to the denoising performance. As a locally adaptive estimation method, the Local Polynomial Approximation-Intersection of Confidence Interval technique can provide anisotropic neighborhoods adapting to image features for pixels in an image in a point-wise manner, within which the image is homogeneous. We combine the non-local means algorithm with this locally adaptive anisotropic estimation method to develop a new denoising approach. It can exclude the pixels whose gray values are different from the one to be restored in the non-local averaging process, and this will alleviate the effect of non-similar pixels and thus enhance the denoising performance.(6) As applications, a signal denoising method combining non-local signal similarities with translation invariant wavelet transform is developed; and also the non-local means algorithm is applied to suppress the poisson noise in PET images.For 1-D signal denoising, signal blocks with similar structures are assembled together to build up groups with strong correlations; and then the translation invariant wavelet transform is applied on these groups to produce, in an enhanced sparsity manner, the transformed coefficients; these coefficients are then hard-thresholded and inverse transformed back into their denoised versions. Considering the overlapping between blocks, two aggregation methods, i.e. simple averaging and weighted averaging are proposed to fuse the different estimates together to get the final estimate. Experimental results illustrate that the proposed method can obtain superior denoising performance compared with the wavelet and translation invariant wavelet based methods. In addition, the non-local means algorithm is applied to remove the poisson noise in PET images. Experimental results for both the test image and real clinical PET images show that the non-local means can remove the noise in PET images efficiently with functional structures well preserved, and achieves better denoising results than median filtering and wiener filtering methods. Therefore, the non-local means algorithm can act as an alternative and potential powerful method for PET image denoising.