Image Transform And Representation Techniques And Their Applications In Image Restoration And Enhancement

Since the creation of photography, a huge number of precious images are accumulated. Because there are various degradation problem in these signals, such as noise, scratch, low-resolution, low contrast and so on, image restoration and enhancement techniques are needed. The research of image restoration and enhancement problem is important for the development of image restoration tech-nology and the protection of visual cultural heritage, which has huge social value and commercial value. Moreover, this research includes image signal analysis, modeling and the solution to a series of ill-posed problems, which has meaningful academic value.The transform and representation techniques of image signal is critical for image restoration and enhancement problem. Signal transform techniques can be classified into geometrical method like Fourier transform, wavelet and so on, and statistical method, such as histogram. By mapping signal from original domain to new space, we can analyze the features of signal from different perspectives and mine the information behind signal. To image signal, an effective transform is beneficial for the establishment of image model and the analysis of statistical or structural feature of image. In this paper, we deeply study the techniques of image signal transform and representation from geometrical and statistical views respectively, and apply them to solve image restoration and enhancement prob-lems, including wave atom transform based image structural artifacts removal, generalized equalization model for image enhancement and fractal analysis model for image super-resolution.Firstly, we introduce a new multi-scale analysis tool called wave atom trans-form and propose an algorithm for structural artifacts removal. Because tradi-tional de-noising methods do not have good performance in complex situation (such as the movie data having multiple artifacts, including noise, scratch, blotch and so on), we need to introduce the geometrical transform into the problem to extract the feature of artifacts. According to its two properties:the direction-ality for high-dimension signal and the sparsity for oscillatory signal, we apply wave atom transform for movie restoration and image de-raining. We propose wave atom based soft-thresholding algorithm for joint movie de-scratching and de-noising. Combining the algorithm with the de-blotching method based on non-parametric model, an automatic movie restoration system is achieved. On the other hand, we design a wave atom based de-raining algorithm, which achieves outstanding performances compared with other existing methods.Secondly, we proposed a histogram-based model called generalized equaliza-tion and apply it on image enhancement. Traditional methods, such as histogram equalization, are likely to over-enhance image and cause tone bias in the enhanced image. To solve these problems, we analyze on the relationships between image histogram and contrast enhancement/white balancing, and establish a general-ized equalization model integrating contrast enhancement and white balancing into a unified framework. We show that many image enhancement tasks can be accomplished by the proposed model using different configurations of parame-ters. Under optimal configuration of parameters, image enhancement algorithm theoretically achieves the best joint contrast enhancement and white balancing result with trading-off between contrast enhancement and tonal distortion. Sub-jective and objective experimental results show favorable performances of the proposed algorithm in image enhancement, especially to under-exposed images, tone biased images and old photos.Finally, besides improving and applying existed techniques, we further pro-posed a new image representation model based on fractal analysis and apply it on image super-resolution. Differing from conventional methods, which always leads to over-smoothed results, in the proposed model we regard pixels of im-age as fractal sets and apply the gradient of image as the measure of these sets. By multi-scale filtering of image, we get the local fractal dimension and fractal length for each set. According to the bi-Lipschitz invariance of fractal dimen-sion, we further deduce the scale-invariance of fractal dimension, which provides super-resolution problem with strong prior knowledge. Moreover, by adding in- variant constraint on fractal length, the gradient of image is enhanced so that the texture part of image is enhanced as well. Compared with other methods, the fractal based representation model and related algorithm obtain superior results in super-resolution and detail enhancement problems.