Image Processing And Application Based On Curvelet Analysis

Curvelet analysis is a new methods of oriented multiscale analysis method, which was developed from wavelet and ridgelet analysis. Ridgelet transform, which has one more parameter--orientation, besides the scale and location, is especially suitable for representing two dimensions signals with linear or hyperplane singularities, and has high approach precision. Curvelet transform is firstly proposed by using the partitioning method and the ridgelet. It is good for describing the curve singularities signals. The anisotropic property makes curvelet suitable for representing the edges of images. The new tight frame of curvelet are the new implementation of curvelet transform based on the frequency domain, are independent of the ridgelet. The new frame of curvelet is called the second generation curvelet, which has less number of parameters and less computation cost when digital implementation. The new frame is the optimal sparse representation of object with discontinuities along curves. As the ridgelet and curvelet analysis theory can describe the smooth image with discontinuities along curves efficiently, it is very useful in image processing.In this paper, we will introduce the ridgelet and curvelet analysis theory, including the base theory, implementation, properties of the ridgelet transform, curvelet transform and the new frame of curvelet. We also describe the applications of ridgelet and curvelet analysis on image processing, including image denoising, image compression, image recognition, image enhancement, image fusion, and so on. In the image processing application based on curvelet analysis, we use the new frame of curvelet to implement the image denoising for experiment. Hard, soft, half-soft, block thresholding algorithms are used for comparing, and genetic algorithms are used to estimate the optimal thresholds. The experiment results are evaluated by the peak signal-to-noise ratio (PSNR) and visual effect of the denoised image, and compared to the wavelet denoising method. The results show that the PSNR and vision of the curvelet denoised image improve a lot, and the curvelet can restore the edge of the image well. In the curvelet thresholding algorithms, the block is best, half-soft and soft is better, hard is good too. In addition, wiener filtering is used to decrease the artifact of the edges to improve the vision of the curvelet denoised images.In this paper, we propose an adaptive curvelet image denoising method, which uses the soft thresholding algorithms to threshold the curvelet coefficients. In the proposed method, new tight frame of curvelet are used to transform the objects, wavelet general cross validation (GCV) is extent to curvelet domain to estimate the optimal thresholds by using the genetic algorithms. The experiment results show that the PSNR and vision of the curvelet denoised images improve a lot, especially at the edge of the image. As the proposed method restores the image directly from the noisy image without estimating the noisy levels or the original image, it is very useful in practical applications.