摘要：

压缩感知主要采用离散余弦变换(DCT)和正交小波进行图像的稀疏表示，但是DCT时频分析性能不佳，小波方向选择性差，不能很好地表示图像边缘的信息。为此，利用Curvelet变换具有的多尺度、各向奇异性、更高稀疏表示性能等特性，提出基于Curvelet变换的图像压缩感知重构算法，采用Curvelet对图像进行稀疏表示和小波域阈值处理，以此解决信号重构噪声问题。实验结果证明，与传统小波变换和Contourlet变换相比，该算法在Lena图像上峰值信噪比平均提高了1.86 dB和1.15 dB。将Curvelet变换应用于压缩感知，能使图像边缘和平滑部分得到最优的表示，图像细节部分重构效果得到大幅提升，有效提高图像整体重构质量。

关键词: 图像处理, 压缩感知, 稀疏表示, 阈值处理, 信号重构, Curvelet变换

Abstract: Discrete Cosine Transform(DCT) and wavelet transform are used for sparse representation, but DCT can’t analyse well in domain of time and frequency. The directional selectivity of wavelet transform is poor and can’t reconstruct edge information well enough. Against the optimization of sparse representation, Curvelet transform has characters of multi-scale, singularity and more sparsity. This paper proposes a compressed sensing reconstruction algorithm based on Curvelet transform, which uses Curvelet transform for sparse representation and thresholding method in wavelet domain to solve the noise problem of signal reconstruction. Results demonstrate that the algorithm gets 1.86 dB higher Peak Signal to Noise Ratio(PSNR) and 1.15 dB higher PSNR compared with traditional wavelet transform and Contourlet transform. As Curvelet transform is applied to compressed sensing, optimal result of edge and smooth part of image are got, also the reconstructed quality of details is increased.

Key words: image processing, compressed sensing, sparse representation, threshold processing, signal reconstruction, Curvelet transform

中图分类号: 

• TP391.41