High-speed continuous imaging systems are constrained by analog-to-digital conversion, storage, and transmission. However, real video signals of objects such as microscopic cells and particles require only a few percent or less of the full video bandwidth for high fidelity representation by modern compression algorithms. Compressed Sensing (CS) is a recent influential paradigm in signal processing that builds real-time compression into the acquisition step by computing inner products between the signal of interest and known random waveforms and then applying a nonlinear reconstruction algorithm. Here, we extend the continuous high-rate photonically-enabled compressed sensing (CHiRP-CS) framework to acquire motion contrast video of microscopic flowing objects. We employ chirp processing in optical fiber and high-speed electro-optic modulation to produce ultrashort pulses each with a unique pseudorandom binary sequence (PRBS) spectral pattern with 325 features per pulse at the full laser repetition rate (90 MHz). These PRBS-patterned pulses serve as random structured illumination inside a one-dimensional (1D) spatial disperser. By multiplexing the PRBS patterns with a user-defined repetition period, the difference signal y_i=phi_i (x_i - x_{i-tau}) can be computed optically with balanced detection, where x is the image signal, phi_i is the PRBS pattern, and tau is the repetition period of the patterns. Two-dimensional (2D) image reconstruction via iterative alternating minimization to find the best locally-sparse representation yields an image of the edges in the flow direction, corresponding to the spatial and temporal 1D derivative. This provides both a favorable representation for image segmentation and a sparser representation for many objects that can improve image compression.
We demonstrate an ultrahigh-rate imaging system applied to very high speed microscopic flows. Chirp processing of ultrafast laser pulses in optical fiber is employed to create pseudorandom spectral patterns at a rate of one unique pattern per pulse. These spectral patterns then serve as structured illumination of the object flows inside a 1D spatial disperser before digitization at a rate of one sample per optical pulse with a fast single pixel photodetector. Diffraction-limited microscopic imaging of flows up to 31.2 m/s is achieved at up to 19.8 and 39.6 Gigapixel/sec rates from a 720 MHz acquisition rate.
Data sets are often modeled as point clouds lying in a high dimensional space. In practice, they usually reside on or near a much lower dimensional manifold embedded in the ambient space; this feature allows for both a simple representation of the data as well as accurate performance for statistical inference procedures such as estimation, regression and classification. In this paper we propose a framework based on geometric multi-resolution analysis (GMRA) to tackle the problem of classifying data lying around a low-dimensional set M embedded in a high-dimensional space RD. We test our algorithms on real data sets and demonstrate its efficacy in the presence of noise.
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