【作者】 成昭；

【导师】 朱砾；

【作者基本信息】 湘潭大学 ， 应用数学， 2011， 硕士

【摘要】 随着科学技术的发展,以及人们需求的日益提高,在科学与工程诸多领域中出现的数据量呈现海量数据的特征.而研究发现,在人们生活中出现的大量数据都存在冗余、相关性强等特点,因此,如何从数据的特点出发,通过研究其稀疏表示的理论与方法,从而极大减少处理时间的空间复杂度与时间计算复杂度就成为现代数学与信息科学诸多研究领域面临的共同问题.图像数据是一种最为常见的信息传输与处理用数据,在信息处理领域有着非常重要的地位.本文通过研究图像数据的特点,针对图像恢复这一传统的图像处理领域开展研究,研究了基于信息稀疏表示算法的超分辨图像重构与图像去噪、图像去模糊方法.1.利用多尺度几何分析中的Bandelet并结合分裂Bregman迭代优化求解算法,建立了一种具有高质量图像恢复性能的超分辨图像重构模型.该方法Bandelet实现图像的高效稀疏表示,利用分裂Bregman方法实现模型的有效优化求解,数值实验表明该算法比已有方法在图像恢复质量方面有一定的提高.2.建立了基于快速Fourier变换(FFT)的非局部分裂技术的图像去噪、去模糊算法.通过提出改进的图像全变分模型,并在此基础上得到了一种图像去噪、去模糊优化模型,该模型可以通过FFT方法求解,从而大大降低了算法的计算复杂性,并通过试验结果验证了方法的有效性.更多还原

【Abstract】 With the development of Scinece and Technology, and more and more increasing of the requirement, cloud data is its mainly characteristic in modern science and engineering. As we known, in general, the data as mentioned above are reduancy and dependence, a common question is to consider theory and method for sprase representation of information so as to decrease complexity of space and time used greatly.Image is a two-dimensional data used information transporation and processing with most commonly used and very improtatntly. In this paper, we study image restoration including super-solution, remove noise and deblurring.1. Combined bandelet in multiscaling geometry analysis and splitted Bregamn optimization algorithm, a type of super-solution mathematical model is developed. Using Bandelet achieves sparse representation of image, and efficiency splitted Bregman algorithm is used to accelerate th computation speed. Numerical examples shows that the quality of reconstruction image is superior known classical algorithm.2. Non-Local model via FFT algorithm for image noise removed and deblurring is proposed. By considering improved Total variation model of image, wo obtain optimization method for image noise removed and deblurring. Since FFT algorithm is used the computational complexity is decreased greatly. Experimenations showns the efficiency of the proposed methods.更多还原