Multiscale Geometric Analysis Based Image De-Noising In A Coherent Optical System

Wavelet analysis is the most successful signal processing technology after Fourier analysis, and it has been applied in many areas. The multiscale geometric analysis is a new focus in recent years and has great potential in image processing because of its'multi-scales and multi-directions decomposition capability. In image denoising, there are many methods in multiscale geometric analysis transform domain, such as methods based on physics models such as the energy model and inter-scale correlation model and methods based on statistical models like the hidden Markov tree model and inverse Gaussian distributions model. But the methods based on physics models study the energy or values of images and noise coefficient which sometimes can not be consistent with the image detail well enough, so that they will damage the image detail. And the statistical models whose corresponding relation to image details still needing to be studied have many parameters and priori limitations for application. In brief, now denoising method in multiscale geometric analysis transform domain still needs to be studied, and the key problem is to find more suitable denoising models and optimize the parameters and algorithms.Coherent optic image processing systems such as the 4f optic system which is based on the Fourier optic theory calculate the image data by optic way. It is a potential subject in information optics for its advantage of parallel processing. Now, researchers can construct many systems for different applications which are sometimes not precise enough. Firstly, current photoelectricity switch devices still process image pixels serially which limit the parallel processing of the whole system. Furthermore, in view of the quality of output images, many problems should be studied. The low-pass band of Furieour lens limits the band width of the output images which require more attention on protection of the useful details when enhancing the noised images. And in such near field coherent optical system, because of the coherent character of lasar, there is not only random noise, but also some low frequency coherent noise in the output images. These make the denoising in coherent system images a diffirent work to the current denoising processing in digital images. This thesis will focus on the second problem——noise reduction, and the protection of the image details and removing of the low frequency noise are excellency of the thesis.Research on the image denoising methods in multiscale geometric analysis area is the work based on advancing signal processing theory and focusing on practically application. It can expand the image denoising technology in multiscale geometric analysis area and also improve the quality of the practical coherent optic image system. It is significant both in theory and practice.The main works of this thesis are:①Variance estimation is an important problem in random noise analysis. The basic idea is to get a sub-image which includes"pure"noise to estimate the variance of the original noise. The traditional method is to obtain the sub-image by sampling the noisy image in spatial or frequency domain, then calculate its variance to replace that of the original noise. It has some limitation when the image has plenty of high frequency details. Based on the traditional frequency sampling method, a new method is proposed. Firstly, choose the first effective oblique high sub-image in 2-D wavelet transform domain as the sub-noise image. Then wipe off the useful image information in it by using the inter-scale correlation to get more"pure"noise sub-image and estimate its variance. Simulation experiments of the real 4f system consistent with the theoretical analysis. The experiment results show that the new method is about 4%～6% more accurate than the traditional method. It is more suitable for the images outputting from a low-pass bandwidth system or images full of details.To get the pre-knowledge for post-correction, according to the real system images, the system error of the 4f coherent optic system is analyzed. The coexistence of low pass error, additional random noise and low frequency coherent noise is indicated. The calculation of low-pass error is deduced; the zero mean Gaussian distribution of random noise is analyzed and its'variance is estimated by the method based on the inter-scale correlation; the original of low frequency coherent noise is indicated, its feature differ from the point-spread function and coherent speckle noise in SAR images is analyzed, and its distribution of stable location and figuration is pointed out. These provide the basis of post-correction.②To remove the noise and protect the image detail better, a geometric continuity based method is proposed. Different with the classic Donoho threshold shrink denoising method in sparse decomposition domain, it adopts a smaller threshold to remove the small amplitude noise to protect the image detail more and protrude the isolation of remnant big amplitude noise, then it uses the hit-or-miss option and corresponding structure element to identify the continuity of image texture to remove the large amplitude isolated noise from the consecutive image detail in the high-frequency sub-band images. Eventually the noise is removed while the image detail is protected. Experiments of routine images and SAR images in curvelet and NSCT domain answer to the theory. Experiment results show that the method can reach the same degree with classic methods in denoising, and is better than classic threshold shrink method in protecting image detail in view of vision and numerical judgment standard (about 0.5~1db of PSNR and 3%~5% of SSIM). It is more suitable for the situation which needs to protect image details extraordinarily.Limited frequency band, random noise and coherent noise feature the conventional 4f information optics system images. The features demand protecting details better when restore those images. Besides, not only the random noise, but also the coherent fringes in low frequency domain should be removed. According to these characters, a new method is proposed to restore 4f system images. Firstly, prior knowledge of the coherent noise is obtained from the step response image of the 4f system. Then the step response and pending image are processed to remove the high frequency random noise in NSCT domain by the method based on geometric continuity with the same parameters. Lastly, based on the linear character of the 4f system, the pixel value of step response image is used from point to point to remove the coherent noise. Experimental results show that the method can restore the image and protect its detail well in view of PSNR (5 dB improved), SSIN (6% improved) and vision. Compared with the current denoising methods in sparse decomposition domain, this method can protect image details better and remove the low frequency noise, furthermore, the use of the step response image reflects the advantage of parallel processing of the 4f system.③For the situation that repeatedly capturing the same object with random noise, to remove the noise and protect image details well, a denoising method based on the fusion of images captured repeatedly is proposed. Taking the random characteristic of noise, it fuses the pixels at the same location of different images to reduce the noise in the way similar to the weighted averaging method. Firstly, the images are decomposed into sub-images in the NSCT domain. In high frequency sub-images, the variance model in neighborhood of corresponding pixels of different images is used to describe the noise density and to modify the fusion weight. In low frequency sub-images, the product of variance to the mean in neighborhood is studied to modify the fusion weight. Lastly, the noise is reduced by the fusion with the similar ideas of the weighted average denoising method, and it is perfect harmless to the image details in theory.By this way, a method based on fusion of multi-spectrum images is proposed. Firstly the multi-spectrum images of experiment based on the image copying character of spatial light modulators are collected. These images contain the same useful image information and noise with similar distribution but different values. Then these images are decomposed into the NSCT domain. The variance in neighborhood is compared to modify the fusion weights in high frequency sub-images so as to remove the random noise. In low frequency sub-image, the neighborhood variance is also studied to modify the multi-level fusion weights to weaken the coherent noise. Lastly, the multi-spectrum images are fused to reduce the random and coherent noise without image distortion. The experiments answer to the theory. The use of the random characteristic of noise in the averaging on time incarnates the idea of exchanging the time domain with space domain. Because it dose not make any calculation on single image plane, it well not change the structure of the image, for which the other denoising methods can not do. It expands the application of image fusion technologies.