基于Curvelet的Stein无偏风险估计图像去噪

Curvelet based Stein's unbiased risk estimate for image denoising

基于Stein无偏风险估计(SURE)和阈值的线性展开式(LET),提出基于Curvelet的SURE-LET图像去噪方法。Curvelet变换实现了对于二阶可微奇异性(C2-singularity)分段连续目标的最优稀疏表达,同时Curvelet阈值保持了曲线奇异性和增强去噪能力。不同于已有算法,SURE方法不必为原始图像假设统计模型。非线性处理在Curve-let变换域执行,最小化操作在图像域进行;去噪过程可以表达为基元去噪过程的线性组合,即LET。SURE和LET两个原则使去噪算法仅解决一个线性方程系统,快速而有效。实验对多幅标准图像进行诸方法的去噪比较,结果表明,该方法优于单纯的Curvelet和SURE-LET去噪方法,相比于Db5小波、BiShrink也具有一定的优势。

An image denoising algorithm based on Stein＇s unbiased risk estimate （SURE） and linear expansion of thresholds （LET） was developed, i.e., curvelet based SURE-LET. The curvelet transform gives the optimal sparse representation of two dimensional piecewise continuous objects with C2-singularities. The curvelet thresholding also preserves boundaries with curve-singularities and enhances the denoising ability. Unlike existing methods, SURE avoids any a priori hypotheses about the noiseless image. Although the nonlinear processing is performed in the transformed domain, the minimization is performed in the image domain. The denoising process can then be expressed as a linear combination of elementary denoising processes as LET. The SURE and LET principles together give a fast, efficient algorithm that only solves a linear system of equations. Digital denoising experiments comparing this algorithm with current algorithms show that the curvelet based SURE-LET is better than the single Curvelet, SURE-LET, Db5 wavelet, and BiShrink methods.