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（MCF）的无透镜照明单像素成像是一种计算成像技术，可在细胞尺度上实现生物样本的内窥镜观测。本研究证明，该技术等同于采集干涉矩阵（一种编码样本图像频谱内容的矩阵）的多重对称秩一投影（SROP）。在该模型中，每个SROP由通过空间光调制器（SLM）塑造入射光波前的复值素描向量诱导产生，而投影的干涉矩阵可采集多达$O(Q^2)$个图像频率（对于含$Q$个纤芯的MCF）。虽然该方案涵盖了先前的传感模态（如波束成形照明下的光栅扫描（RS）成像），但我们证明：收集$M$个随机SLM配置的测量值（即获取$M$个SROP），即可在$M$和$Q$随图像稀疏度呈对数线性增长时估计目标图像。该结论通过理论分析（基于传感方案特定约束等距性分析）与蒙特卡洛实验双重验证。在实践层面，我们实现了对理论模型特定偏差具有鲁棒性、且与成像阶段所用素描向量无关的传感系统单次校准。在实际MCF系统上的实验结果验证了该成像方法在基准图像上的有效性。