一种基于小波和矩阵型扩散的图像放大

提出了一种基于小波多分辨分析和矩阵型扩散的图像放大方法.该方法把原图像作为放大图像的小波低频子带,初始高频置零小波重构,用矩阵型扩散方程处理后小波分解,得到估计的高频再与原图像重构.在扩散中取矩阵型扩散的扩散系数,选择其特征根,使扩散在垂直于边缘方向梯度较大时为逆扩散以锐化边缘,而沿边缘方向为正向扩散以增强边缘；同时提出了放大图像与原图像的一种相似性标准.该方法在放大图像的同时既去除了噪音又有效保持了边缘.数值实验结果证实,此方法为一个有效地图像放大方法.

Image Zooming Based on Wavelet and Matrix-valued Diffusion Equation

Based on wavelet multi-resolution analysis and matrix-valued diffusion equation,an image zooming model was presented.The original image was presented as the low pass filter of the wavelet analysis,and its high pass filters were zeros.The matrix-valued diffusion equation was used to the zoomed image and then wavelet analysis,the obtained high pass filter was used as the estimated high pass filter with the original image can be used to reconstruct.The new model adopts the idea of the property like the edge-enhancing diffusivity that the eigenvalues are designed so that the new diffusion coefficients have negative values in the gradient direction,when the gradient is large,to sharpen the edges and positive ones along the edge direction to enhance them; simultaneously a comparability criterion of the zoomed image and the original one were proposed.So the image was denoised and edge preserved as well as zoomed.Some numerical experiments illustrate that the proposed methods is a valid new image zoomed algorithm.