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1.1 Terahertz imaging and compressive sensing

A newly developed theory in signal processing called compressive sensing (CS) has
emerged in recent years. CS enables reconstruction of an image using many fewer
measurements than are traditionally required [8,9]. The principle behind applying CS
to the design of imaging systems is analogous to a two-step image encoding∕decoding
process: one can view image acquisition as the encoding step, and image reconstruc-
tion as the decoding step. For image acquisition, the goal is to efficiently capture the
information about an object into a small set of measurements. For image reconstruc-
tion, CS relies on the common spatial structures present in real-world images. Based
on the knowledge of these spatial structures, the CS reconstruction scheme “decode”
the small set of measurements to recover a full image of the original object through
an optimization procedure.

In general, when the number of measurements is significantly smaller than the total
dimension of the image, the image reconstruction problem is undetermined, i.e., it
has more than one solution. The CS encoding procedure (image acquisition) needs to
ensure a one-to-one mapping between the class of images with certain spatial structure
and the measurement space to allow exact image recovery. This thesis chooses two
particular choices of encoding as the foundation to build CS THz imaging systems
which acquires image fast, while keeping the hardware as simple as possible. The first
CS Fourier THz imaging system acquires image data on the Fourier plane, and can
reconstruct images with only a small subset of the complete 2-D Fourier transform
data. Compared to traditional timed-domain raster scanning or uniform Fourier
sampling on the full grid, partial sampling along a random path on the Fourier plane
in this system can reduce the image acquisition time significantly. The second single-
pixel CS imaging system performs compression simultaneously with image sampling

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