Lensless illumination single-pixel imaging with a multicore fiber (MCF) is a computational imaging technique that enables potential endoscopic observations of biological samples at cellular scale. In this work, we show that this technique is tantamount to collecting multiple symmetric rank-one projections (SROP) of an interferometric matrix--a matrix encoding the spectral content of the sample image. In this model, each SROP is induced by the complex sketching vector shaping the incident light wavefront with a spatial light modulator (SLM), while the projected interferometric matrix collects up to $O(Q^2)$ image frequencies for a $Q$-core MCF. While this scheme subsumes previous sensing modalities, such as raster scanning (RS) imaging with beamformed illumination, we demonstrate that collecting the measurements of $M$ random SLM configurations--and thus acquiring $M$ SROPs--allows us to estimate an image of interest if $M$ and $Q$ scale log-linearly with the image sparsity level This demonstration is achieved both theoretically, with a specific restricted isometry analysis of the sensing scheme, and with extensive Monte Carlo experiments. On a practical side, we perform a single calibration of the sensing system robust to certain deviations to the theoretical model and independent of the sketching vectors used during the imaging phase. Experimental results made on an actual MCF system demonstrate the effectiveness of this imaging procedure on a benchmark image.

翻译：多芯光纤无透镜照明单像素成像是一种计算成像技术，能够实现细胞尺度生物样本的潜在内窥镜观测。本研究证明，该技术等价于收集干涉矩阵（编码样本图像频谱信息的矩阵）的多个对称秩一投影。在该模型中，每个对称秩一投影由空间光调制器塑造入射光波前的复值素描向量诱导产生，而被投影的干涉矩阵针对含Q根纤芯的多芯光纤可收集多达O(Q²)个图像频率分量。虽然该方案涵盖了先前的传感模式（如波束成形照明的光栅扫描成像），我们证明：收集M个随机空间光调制器构型的测量值（即获取M个对称秩一投影），可在M和Q与图像稀疏度呈对数线性缩放时估计目标图像。该结论通过理论层面的特定受限等距性分析传感方案，以及大量蒙特卡洛实验得到双重验证。在实践层面，我们实现了对理论模型特定偏差具有鲁棒性且不依赖于成像阶段素描向量的单次传感系统标定。基于实际多芯光纤系统的实验结果展示了该成像方法在基准图像上的有效性。