基于傅里叶剪切波变换的图像去卷积算法.doc

基于傅里叶-剪切波变换的图像去卷积算法 研究与仿真 摘要：受成像条件、外部噪声以及人为因素的影响，人们获取到的图像常常会出现不同程度的失真，如图像含有噪声、模糊不清。噪声和模糊的存在降低了图像的视觉质量，影响了图像的后续处理。为改善图像质量，尽可能减少失真对图像后续处理的影响，对图像进行去噪和去模糊处理就成为图像预处理过程中一项非常重要的工作。小波变换因其多分辨特性而被广泛应用于图像去噪和去模糊。然而，小波变换只能表示图像中的点状奇异，而不能有效地表示曲线奇异。新近出现的剪切波变换则有效地克服了小波变换的缺陷。 在本文中，我们使用了一种基于剪切波变换的图像去卷积方法。模糊图像首先被投射到傅里叶域，进行正则化反演去模糊。之后剪切波再将图像分解到各个尺度和方向上，剪切波域的阈值将有色噪声收缩。为了提高估计质量，我们引入一种新型剪切波变换-离散不可分离剪切波变换，相对之前的剪切波变换，其方向指向性更好。但是Tikhonov正则限制了算法的提升空间，因此本文提出了一种将较为先进的正则化方法LPA-ICI与DNST结合的算法。大量的实验数据说明本文的去卷积算法在图像去模糊方面的潜力。 关键词：去卷积；去噪；剪切波变换；Tikhonov正则化； Abstract：Images are often corrupted by noise and blur due to the undesired conditions for image acquisition, processing and transmission. The noise and blur in images have severely degraded image quality and affected the subsequent image processing tasks. Thus noise and blur reduction has been a very important pre-processing step for improving the quality of images. In the past decade, the wavelet transform has been successfully used in image denoising and deblurring due to its multiresolution capability. However, despite its remarkable success in dealing with pointwise singularities, the standard separable wavelet transform fails to provide an optimal sparse representation for images that contain other types of singularities. Shearlets, a new directional multiresolution transform, can efficiently represent the directional information of images. In this paper, we consider a approach to image deconvolution based on shearlet transform. The deblurring is accomplished when the blurred image is first projected onto a Fourier domain, following Tikhonov regularized inversion, the colored noise is then suppressed using a shearlet domain based thresholding. To improve the estimating capability, we introduce a new shearlet transform associated with a nonseparable shearlet generator, which improves the directional selectivity of previous shearlet transforms. However,the above method cannot improve much due to the limitation of Tikhonov regulariza