【作者】 尚倩；

【导师】 练秋生；

【作者基本信息】 燕山大学 ， 电路与系统， 2010， 硕士

【摘要】 寻求客观事物的“稀疏”表示方法一直是机器视觉、数据压缩等领域专家学者致力于研究的目标。由于图像稀疏表示的优良特性,目前针对图像的稀疏表示已经发展了多种算法。图像的稀疏表示也已经成功应用于图像的压缩、去噪、识别等。由于图像的稀疏表示在图像处理中的成功应用,已经引起越来越多研究人员的重视,形成对图像稀疏分解研究的热潮。对于分段光滑信号,小波提供了一种非常简单而有效的表示方法,然而传统意义上的小波变换在高维情况下并不是最优的或者说是“最稀疏”的函数表示方法。过完备多分辨率变换能够充分利用函数本身信息,对特定的函数类达到最优逼近。不同的变换各自适合表示不同的图像特征,这给图像稀疏表示提供了更有力的理论和方法。此外,生物视觉系统的发展和进化与其感知的外界环境(自然图像)密切相关。实验表明,自然图像的非高斯统计特性与神经元的稀疏编码方式相对应。首先,本文提出利用过完备多分辨率变换并结合视觉特性的图像稀疏表示方法。该算法用双树复数小波模拟视觉皮层简单细胞的感受野,结合相邻细胞间抑制和增强特性,用局部竞争抑制的方法从变换系数中选取少量系数稀疏表示图像。实验结果表明,其重构图像的效果较其它方法有明显的改善。其次,本文根据Marr初级视觉理论,在一种能够从多尺度描述一幅图像的一种新的复数小波——Marr-like小波金字塔以及一种新的适应性Harr小波变换——Tetrolet变换的基础上,提出将Marr-like小波金字塔分解与Tetrolet相结合的图像稀疏表示方法。数值实验表明该算法能够更好的匹配图像的几何特征,具有更好的可控性和图像重构效果。更多还原

【Abstract】 In the fields of machine vision and data compression, seeking for the“sparse”representation of the objective things has been the domain to which the experts and scholars devoted. Nowadays, due to the excellent characteristics of image sparse representation, numerous algorithms have been developed. As a result of the successful application of sparse representation of images in image compression, denoising, recognition, etc. an increasing number of researchers begin to attach importance to this field and form a new upsurge.For a piecewise smooth signal, wavelet provides a very simple and effective method. However, in high-dimension circumstances, conventional wavelet transform is not the optimal or the“most sparse”representation of functions. Overcomplete multiresolution transform could take full advantage of the information, which is contained in the function itself, and achieve the optimal approximation to the specific functions. Different transforms are appropriate for describing diversified characteristics of images, which provide powerful theories and methods for sparse representation of images. In addition, the development and evolution of biological visual system is closely related to the perceived external environment (natural images). Experiments have indicated that non-gaussian statistical properties of natural images have some correspondence with the sparse coding methods of neurons.Firstly, a sparse representation scheme of images which is inspired from overcomplete multiresolution transforms combined with visual characteristic, is proposed. The algorithm models simple cell receptive fields through Dual-Tree Complex Wavelets. The model also incorporates inhibition and facilitation interactions between neighboring cells to choose a number of coefficients of transformation to achieve the sparse representation of initial images by utilizing the local competition and inhibition method. The experiment results show that the proposed scheme outperforms others.Secondly, according to Marr’s theory of preliminary vision, based on a new kind of complex wavelet—Marr-like wavelet, which could describe an image from multiscales, and a novel adaptive Harr-type wavelet transform—Tetrolet, we propose a new method for sparse representation of images which combines the two methods mentioned above. Numerical results show this method is capable of matching the geometrical characteristics of images and has better steerability as well as reconstruction result.更多还原