Browsing by Subject "compressive sampling"

This work focuses on the construction and application of coded apertures to compressive X-ray tomography. Coded apertures can be made in a number of ways, each method having an impact on system background and signal contrast. Methods of constructing coded apertures for structuring X-ray illumination and scatter are compared and analyzed. Apertures can create structured X-ray bundles that investigate specific sets of object voxels. The tailored bundles of rays form a code (or pattern) and are later estimated through computational inversion. Structured illumination can be used to subsample object voxels and make inversion feasible for low dose computed tomography (CT) systems, or it can be used to reduce background in limited angle CT systems.

On the detection side, coded apertures modulate X-ray scatter signals to determine the position and radiance of scatter points. By forming object dependent projections in measurement space, coded apertures multiplex modulated scatter signals onto a detector. The multiplexed signals can be inverted with knowledge of the code pattern and system geometry. This work shows two systems capable of determining object position and type in a 2D plane, by illuminating objects with an X-ray `fan beam,' using coded apertures and compressive measurements. Scatter tomography can help identify materials in security and medicine that may be ambiguous with transmission tomography alone.

This dissertation describes two computational sensors that were used to demonstrate applications of generalized sampling of the optical field. The first sensor was an incoherent imaging system designed for compressive measurement of the power spectral density in the scene (spectral imaging). The other sensor was an interferometer used to compressively measure the mutual intensity of the optical field (coherence imaging) for imaging through turbulence. Each sensor made anisomorphic measurements of the optical signal of interest and digital post-processing of these measurements was required to recover the signal. The optical hardware and post-processing software were co-designed to permit acquisition of the signal of interest with sub-Nyquist rate sampling, given the prior information that the signal is sparse or compressible in some basis.

Compressive spectral imaging was achieved by a coded aperture snapshot spectral imager (CASSI), which used a coded aperture and a dispersive element to modulate the optical field and capture a 2D projection of the 3D spectral image of the scene in a snapshot. Prior information of the scene, such as piecewise smoothness of objects in the scene, could be enforced by numerical estimation algorithms to recover an estimate of the spectral image from the snapshot measurement.

Hypothesizing that turbulence between the scene and CASSI would introduce spectral diversity of the point spread function, CASSI's snapshot spectral imaging capability could be used to image objects in the scene through the turbulence. However, no turbulence-induced spectral diversity of the point spread function was observed experimentally. Thus, coherence functions, which are multi-dimensional functions that completely determine optical fields observed by intensity detectors, were considered. These functions have previously been used to image through turbulence after extensive and time-consuming sampling of such functions. Thus, compressive coherence imaging was attempted as an alternative means of imaging through turbulence.

Compressive coherence imaging was demonstrated by using a rotational shear interferometer to measure just a 2D subset of the 4D mutual intensity, a coherence function that captures the optical field correlation between all the pairs of points in the aperture. By imposing a sparsity constraint on the possible distribution of objects in the scene, both the object distribution and the isoplanatic phase distortion induced by the turbulence could be estimated with the small number of measurements made by the interferometer.