Terahertz imaging with compressed sensing and phase retrieval

Abstract

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.

Recent advances in terahertz technology for biomedical applications

“…Another option therefore is to alter the imaging paradigm itself, relying on the sparsity of spatial frequencies in most images to perform compressed sensing (CS). First demonstrated at THz frequencies in 2008 (47,48) this technique has since been demonstrated, among others, by using either random mechanically developed and switched masks (49), a spinning disk set (50), electrically gated graphene modulator arrays (51) and by photoexciting a silicon substrate with an optical pattern (52). The techniques demonstrated here rely on a binary state for each pixel, i.e., the pixels are either on and off, in order to eventually separate the response of each pixel through the linear combinations recorded in the measurements.…”

Sparse spectral factorization: Unicity and reconstruction algorithms

“…Here, we investigate the discrete case, under the more challenging setting of unknown supports, and provide concrete algorithms for signal reconstructions. The sparsity prior has also been considered in a recent work [5] to derive efficient acquisition schemes for phase retrieval. In general, the autocorrelation of a K-sparse signal is also sparse, consisting of up to K 2 nonzero elements, and thus can be determined from O(K 2 log(N )) Fourier samples [5].…”

“…The sparsity prior has also been considered in a recent work [5] to derive efficient acquisition schemes for phase retrieval. In general, the autocorrelation of a K-sparse signal is also sparse, consisting of up to K 2 nonzero elements, and thus can be determined from O(K 2 log(N )) Fourier samples [5]. Once the autocorrelation is obtained, the actual spectral factorization (or phase retrieval) in that work is still done by using classical algorithms [1].…”

Sparse kronecker pascal measurement matrices for compressive imaging

“…The compressibility of the real-word images shows the potential for optical compressive imaging. In the past few years, CS technique has made great progress in many research fields, which include terahertz compressive imaging [3], spectral imaging [4], single pixel imaging [5] and infrared imaging [6]. Some optical imaging applications have been implemented in specific physical experiments.…”