论文标题
冗余基础和收缩函数在图像DeNoising中的作用
The Role of Redundant Bases and Shrinkage Functions in Image Denoising
论文作者
论文摘要
小波denoisising是一种经典有效的方法，用于减少图像和信号中的噪声。建议在1994年建议，使用一组标量收缩函数（SFS）来纠正转换域中嘈杂图像的系数。大量论文涉及SFS的最佳形状和所使用的转换，众所周知，将SFS应用于冗余基础，可提供改进的结果。本文提供了所用转换，最佳收缩函数与优化域之间的相互关系的完整图片。特别是，我们表明，对于子带优化，每个SF都针对特定频段进行了优化，优化空间域中的SF始终比在变换域中优化SFS始终更好或等同。对于冗余基础，我们提供了相对于统一基础的预期去质量增益作为冗余率的函数。
Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image in the transform domain, using a set of scalar shrinkage function (SFs). A plethora of papers deals with the optimal shape of the SFs and the transform used, where it is known that applying the SFs in redundant bases provides improved results. This paper provides a complete picture of the interrelations between the transform used, the optimal shrinkage functions, and the domains in which they are optimized. In particular, we show that for subband optimization, where each SF is optimized independently for a particular band, optimizing the SFs in the spatial domain is always better than or equal to optimizing the SFs in the transform domain. For redundant bases, we provide the expected denoising gain we may achieve, relative to the unitary basis, as a function of the redundancy rate.
