论文标题
在压缩感中利用小波变换的结构
Utilizing the Wavelet Transform's Structure in Compressed Sensing
论文作者
论文摘要
压缩传感已授权质量图像重建，但数据样本比以前更少。这些技术依赖于稀疏的线性变换。 Daubechies小波变换是用于此目的的常见稀疏转换。在这项工作中，我们利用了该小波转换的结构，并确定仿射变换，从而增加了结果的稀疏性。包含这种仿射转化后，我们修改了由此产生的优化问题，以符合基础追求denoising问题的形式。最后，从理论上讲，这会在重建的误差上产生一个下限，并且在解决此修改后的问题中产生相同采样模式的较高质量的图像。
Compressed sensing has empowered quality image reconstruction with fewer data samples than previously though possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is a common sparsifying transformation used for this purpose. In this work, we take advantage of the structure of this wavelet transform and identify an affine transformation that increases the sparsity of the result. After inclusion of this affine transformation, we modify the resulting optimization problem to comply with the form of the Basis Pursuit Denoising problem. Finally, we show theoretically that this yields a lower bound on the error of the reconstruction and present results where solving this modified problem yields images of higher quality for the same sampling patterns.
