基于压缩感知与扩展小波树的自适应压缩成像

为了在现有的采样条件下，通过新的压缩采样方式获得计算量小且质量更好的图像，提出了基于压缩感知与扩展小波树的自适应压缩成像方法。首先将图像投影到分区控制的DMD上，获得图像在低分辨率下的测量值，并通过压缩感知重构算法重构出低分辨图像，接着利用扩展小波树预测重要小波位置，通过DMD在小波域采样获取图像的细节信息，最后由小波逆变换恢复高分辨率图像。将该方法与最小化全变分算法（TVAL3）和近来提出的基于扩展小波树的自适应成像算法（EWT-ACS）效果进行对比，实验结果表明，以boat图像为例，在压缩感知采样率为0.75，整体采样率为10%的无噪声条件下，该方法相较于TVAL3、EWT-ACS算法信噪比提高了4.63 dB和2.87 dB，在附加噪声条件下成像效果也较好。该方法能极大地降低压缩感知重建算法的运行时间，同时减少采样次数，具有较好的抗噪性。

Adaptive Compression Sampling with Compressive Sensing and Extended Wavelet Tree

In order to obtain the image with a small amount of computation and better quality through a new compression sampling method under the existing sampling conditions. we proposed a new algorithm to achieve the goal. First, the image was projected onto the partitioned digital micro-mirror device(DMD), and the measured values of the image were obtained at low resolution. The low resolution image was reconstructed by the compressive sensing reconstruction algorithm. Then the important wavelet positions were predicted by the extended wavelet tree, and the digital micro-mirror device was used in the wavelet domain. Sampling acquired the details of the image, and finally the high-resolution image was restored by inverse wavelet transform. We compared our algorithm with TVAL3 which was the most commonly used minimization total variational algorithm in compressive sensing image reconstruction and EWT-ACS which was the recently proposed extended wavelet tree-based adaptive imaging algorithm. The results show that when the objective is image boat without noise, our algorithm is 4.36 dB and 2.87 dB higher than TVAL3 algorithm and EWT-ACS algorithm when the compressed sensing ratio is 0.75 and the total sampling ratio is 10%. We also analyzed the results of three algorithms when the image is contaminated by noise. This method greatly reduces the running time of compressive sensing reconstruction algorithm, while reducing the number of sampling, has a good anti-noise.