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We describe a novel, high-speed pulsed terahertz (THz) Fourier imaging system based on compressed sensing (CS), a new signal processing theory, which allows image reconstruction with fewer samples than traditionally required. Using CS, we successfully reconstruct a 64 x 64 image of an object with pixel size 1.4 mm using a randomly chosen subset of the 4096 pixels, which defines the image in the Fourier plane, and observe improved reconstruction quality when we apply phase correction. For our chosen image, only about 12% of the pixels are required for reassembling the image. In combination with phase retrieval, our system has the capability to reconstruct images with only a small subset of Fourier amplitude measurements and thus has potential application in THz imaging with cw sources.
We describe a new terahertz imaging method for high-speed image acquisition using a compressed sensing phase retrieval algorithm. This technique permits image reconstruction using a limited and randomly chosen subset of a Fourier image.With applications to homeland security, medical imaging, and quality control of packaged goods, commercial time-domain THz imaging systems can achieve a spatial resolution of less than 1 mm. However, these systems are generally limited by slow image acquisition rate [1,2]. Meanwhile, developments of THz imaging techniques using more sophisticated image processing approaches, such as the Radon transform [3,4] and interferometric imaging [5], have shown preliminary successes but face similar limitations in speed, resolution and/or hardware requirements. Here we describe a new approach which addresses these problems by partial sampling of the amplitude image in the Fourier plane and reconstruction of the target based on its spatial structure. This work is motivated by the possibility of reconstructing an image using many fewer measurements than are traditionally required.Integral to our approach is a new signal processing scheme that combines the recent theory of compressed sensing (CS) [6-8] with traditional phase retrieval (PR) algorithms [9]. Traditional PR algorithms recover the Fourier phase from modulus-only measurements of an image's entire Fourier transform. CS theory enables image recovery from a small, random subset of Fourier measurements (magnitude and phase). In general, an infinite number of signals can be found that match these few measurements; CS uses an optimization procedure to find the "best" solution. This notion of "best" is based on assumptions of the objects' spatial structure, e.g., the sparsest solution in terms of some basis. We combine CS and PR to reconstruct the object with a small subset of the Fourier transform modulus. Our Compressed Sensing Phase Retrieval algorithm (CSPR) iterates in a way similar to the classic Hybrid Input-Output (HIO) algorithm [6] in order to find the phase of the limited measurements, but in each step also performs a CS optimization. The CS-scheme we use is orthogonal matching pursuit (OMP) [10].Our imaging system consists of a THz transmitter, a receiver, and two lenses, one of which collimates the THz beam while the other focuses the beam (Fig.
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