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，该技术相当于采集干涉矩阵——编码样本图像频谱内容的矩阵——的多个对称秩一投影。在此模型中，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草图向量诱导，而投影的干涉矩阵可采集至多$O(Q^2)$个图像频率（对应$Q$芯多芯光纤）。虽然该方案覆盖了先前的传感模态（如波束成形照明下的光栅扫描成像），我们证明：通过收集$M$个随机空间光调制器配置的测量值（即获取$M$个对称秩一投影），当$M$和$Q$随图像稀疏度呈对数线性增长时，即可估计目标图像。该论证通过传感方案的特定限制等距分析理论推导与大量蒙特卡洛实验共同实现。在实践层面，我们对该传感系统进行单次标定，使其对理论模型的某些偏差具有鲁棒性，且标定过程与成像阶段使用的草图向量无关。基于实际多芯光纤系统的实验结果，展示了该成像流程在基准图像上的有效性。