基于压缩感知的菲涅尔孔径编码无透镜成像(特邀)  

Fresnel Zone Aperture Lensless Imaging by Compressive Sensing(Invited)

作　　者：吴佳琛 曹良才[1] WU Jiachen;CAO Liangcai(State Key Laboratory of Precision Measurement Technology and Instruments,Department of Precision Instruments,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学精密仪器系精密测试技术及仪器国家重点实验室,北京100084

出　　处：《光子学报》2022年第7期261-270,共10页Acta Photonica Sinica

基　　金：国家重点研究发展计划(No.2021YFB2802000)。

摘　　要：为了降低菲涅尔孔径编码成像的传输带宽,改善小尺寸像感器拼接成像质量,提出菲涅尔孔径编码成像的压缩感知重建算法。基于压缩感知理论框架对部分采样的编码图像重建可行性进行分析,指出压缩感知重建误差随波带片常数缩小而降低。根据重建图像中孪生像和原始像在梯度域稀疏性的差异,引入全变差正则化实现抑制孪生像的效果。建立压缩感知理论框架下图像重建目标函数,利用交替方向乘子法进行求解。结合编码图像的能量分布和采样模式的可实现性,测试了矩形采样和辐射线采样两种模式,对不同采样数据量下重建图像质量进行分析。结果表明,辐射线采样模式相比矩形采样模式具有更高的图像采样效率,且仅通过7.3%的实验测量数据就可以获得质量良好的图像,为多块小尺寸像感器拼接成像提供了理论基础,有利于拓展编码掩膜无透镜成像的应用领域。The Fresnel Zone Aperture(FZA)lensless imaging utilizes a Fresnel zone plate to encode the incident light as a holographic pattern. The image could be reconstructed by using holographic imaging methods. Compared with other mask-based lensless imaging methods,FZA imaging does not need any calibration. However,the inherent twin-image effect in in-line holography degrades the reconstructed image quality. In addition,the frequency of recorded fringes becomes higher with the increase of the FZA radius. Thus,a large size of the sensor could record fine fringes and obtain a high-resolution image.Because of the expensive cost of a large-size sensor,using several separate small-size sensors instead of a large-size sensor is an alternate scheme to realize high-resolution imaging. Since only partial measurements could be obtained by multiple sensors,the compressive sensing technique should be utilized for image reconstruction. The restricted isometry property is the sufficient condition of compressive sensing,unfortunately, this property is difficult to verify for a given matrix. Since the Gaussian random measurement matrix is proved to be a universal compressive sensing matrix,it is used as a reference to test the signal recovery ability of the FZA sensing matrix. The results show the reconstruction error decreases with the shrinking of the FZA constant. When the FZA constant is equal to 0.5 mm,the reconstruction performance is almost consistent with the Gaussian random matrix. Thus,compressive reconstruction for FZA imaging is feasible. Since the twin image,the original image and the sum of the two satisfy the forward model,image reconstruction belongs to an ill-posed problem because of multiple solutions. The regularization method is necessary to keep the solutions unique and stable. According to the sparsity difference between the twin image and the original image in the gradient domain,Total Variation(TV)regularization is introduced to suppress the twin image. The objective function of image reconstruction consists of

关 键 词：无透镜成像 压缩感知 菲涅尔波带片 编码掩膜 图像重建 

分 类 号：O439[机械工程—光学工程]