Compressed sensing on terahertz imaging

Most terahertz (THz) time-domain (pulsed) imaging experiments that have been performed by raster scanning the object relative to a focused THz beam require minutes or even hours to acquire a complete image. This slow image acquisition is a major limiting factor for real-time applications. Other systems using focal plane detector arrays can acquire images in real-time, but they are too expensive or are limited by low sensitivity in the THz range. More importantly, such systems cannot provide spectroscopic information of the sample. To develop faster and more efficient THz time-domain (pulsed) imaging systems, this research used random projection approach to reconstruct THz images from the synthetic and real-world THz data based on the concept of compressed/compressive sensing/sampling (CS). Compared with conventional THz time-domain (pulsed) imaging, no raster scanning of the object is required. The simulation results demonstrated that CS has great potential for real-time THz imaging systems because its use can dramatically reduce the number of measurements in such systems. We then implemented two different CS-THz systems based on the random projection method. One is a compressive THz time-domain (pulsed) spectroscopic imaging system using a set of independent optimized masks. A single-point THz detector, together with a set of 40 optimized two-dimensional binary masks, was used to measure the THz waveforms transmitted through a sample. THz time- and frequency-domain images of the sample comprising 20×20 pixels were subsequently reconstructed. This demonstrated that both the spatial distribution and the spectral characteristics of a sample can be obtained by this means. Compared with conventional THz time-domain (pulsed) imaging, ten times fewer THz spectra need to be taken. In order to further speed up the image acquisition and reconstruction process, another hardware implementation - a single rotating mask (i.e., the spinning disk) with random binary patterns - was utilized to spatially modulate a collimated THz. After propagating through the sample, the THz beam was measured using a single detector, and a THz image was subsequently reconstructed using the CS approach. This demonstrated that a 32×32 pixel image could be obtained from 160 to 240 measurements. This spinning disk configuration allows the use of an electric motor to rotate the spinning disk, thus enabling the experiment to be performed automatically and continuously. To the best of our knowledge, this is the first experimental implementation of a spinning disk configuration for high speed compressive image acquisition. A three-dimensional (3D) joint reconstruction approach was developed to reconstruct THz images from random/incomplete subsets of THz data. Such a random sampling method provides a fast THz imaging acquisition and also simplifies the current THz imaging hardware implementation. The core idea is extended in image inpainting to the case of 3D data. Our main objective is to exploit both spatial and spectral/temporal information for recovering the missing samples. It has been shown that this approach has superiority over the case where the spectral/temporal images are treated independently. We first proposed to learn a spatio-spectral/temporal dictionary from a subset of available training data. Using this dictionary, the THz images can then be jointly recovered from an incomplete set of observations. The simulation results using the measured THz image data confirm that this 3D joint reconstruction approach also provides a significant improvement over the existing THz imaging methods.