Kerkil Choi

Compressive sampling enables signal reconstruction using less than one measurement per reconstructed signal value. Compressive measurement is particularly useful in generating multidimensional images from lower dimensional data. We demonstrate single frame 3D tomography from 2D holographic data.

A coded aperture snapshot spectral imager (CASSI) estimates the three-dimensional spatiospectral data cube from a snapshot two-dimensional coded projection, assuming that the scene is spatially and spectrally sparse. For less spectrally sparse scenes, we show that the use of multiple nondegenerate snapshots can make data cube recovery less ill-posed, yielding improved spatial and spectral reconstruction fidelity. Additionally, data acquisition can be easily scaled to meet the time/resolution requirements of the scene with little modification or extension of the original CASSI hardware. A multiframe reconstruction of a 640 × 480 × 53 voxel datacube with 450-650 nm white-light illumination of a scene reveals substantial improvement in the reconstruction fidelity, with limited increase in acquisition and reconstruction time.

Compressive holography enables 3D reconstruction from a single 2D holographic snapshot for objects that can be sparsely represented in some basis. The snapshot mode enables tomographic imaging of microscopic moving objects. We demonstrate video-rate tomographic image acquisition of two live water cyclopses with 5.2 μm spatial resolution and 60 μm axial resolution.

We propose an estimation-theoretic approach to the inference of an incoherent 3D scattering density from 2D scattered speckle field measurements. The object density is derived from the covariance of the speckle field. The inference is performed by a constrained optimization technique inspired by compressive sensing theory. Experimental results demonstrate and verify the performance of our estimates.

Diverse physical measurements can be modeled by X-ray transforms. While X-ray tomography is the canonical example, reference structure tomography (RST) and coded aperture snapshot spectral imaging (CASSI) are examples of physically unrelated but mathematically equivalent sensor systems. Historically, most x-ray transform based systems sample continuous distributions and apply analytical inversion processes. On the other hand, RST and CASSI generate discrete multiplexed measurements implemented with coded apertures. This multiplexing of coded measurements allows for compression of measurements from a compressed sensing perspective. Compressed sensing (CS) is a revelation that if the object has a sparse representation in some basis, then a certain number, but typically much less than what is prescribed by Shannon's sampling rate, of random projections captures enough information for a highly accurate reconstruction of the object. This paper investigates the role of coded apertures in x-ray transform measurement systems (XTMs) in terms of data efficiency and reconstruction fidelity from a CS perspective. To conduct this, we construct a unified analysis using RST and CASSI measurement models. Also, we propose a novel compressive x-ray tomography measurement scheme which also exploits coding and multiplexing, and hence shares the analysis of the other two XTMs. Using this analysis, we perform a qualitative study on how coded apertures can be exploited to implement physical random projections by "regularizing" the measurement systems. Numerical studies and simulation results demonstrate several examples of the impact of coding.