Dr. Kerkil Choi Profile

Dr. Kerkil Choi

Postdoctoral Associate at Duke Univ

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Proceedings Article | 28 August 2010 Paper

Sparse aperture coding for compressive sampling

David Brady, Alexander Mrozack, Kerikil Choi

Proceedings Volume 7818, 78180D (2010) https://doi.org/10.1117/12.862159

KEYWORDS: Modulation transfer functions, Imaging systems, Spatial frequencies, Signal to noise ratio, Imaging spectroscopy, Fourier transforms, Sensors, Photons, Objectives, Systems modeling

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For many years, the basic goal of sparse aperture design has been to maximize the support of the modulation transfer function (MTF). Golay apertures and related nonredundant arrays are typically used to achieve this objective. Unfortunately, maximizing the support of the MTF has the necessary effect of decreasing the magnitude of the MTF at mid-band spatial frequencies. Fienup has shown that the decreased magnitude of the MTF for nonredundant arrays contributes as much as reduced throughput to the loss of SNR in sparse apertures relative to full aperture systems. This paper considers the use of periodic sparse arrays to improve the mid-band MTF at the cost of reduced spatial frequency coverage. We further consider methods to recover lost spatial frequencies using multispectral and multiframe sampling and decompressive inference.

Proceedings Article | 25 August 2009 Paper

Coded aperture computed tomography

Kerkil Choi, David Brady

Proceedings Volume 7468, 74680B (2009) https://doi.org/10.1117/12.825277

KEYWORDS: X-rays, Sensors, Coded apertures, Tomography, 3D metrology, Transform theory, 3D modeling, Multiplexing, Compressed sensing, Computed tomography

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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.

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