Abstract-Approximate Message Passing for Indoor THz Channel Estimation

Viktoria Schram, Ali Bereyhi, Jan-Nico Zaech, Ralf R. Müller, Wolfgang H. Gerstacker

https://arxiv.org/abs/1907.05126

Compressed sensing (CS) deals with the problem of reconstructing a sparse vector from an under-determined set of observations. Approximate message passing (AMP) is a technique used in CS based on iterative thresholding and inspired by belief propagation in graphical models. Due to the high transmission rate and a high molecular absorption, spreading loss and reflection loss, the discrete-time channel impulse response (CIR) of a typical indoor THz channel is very long and exhibits an approximately sparse characteristic. In this paper, we develop AMP based channel estimation algorithms for indoor THz communications. The performance of these algorithms is compared to the state of the art. We apply AMP with soft- and hard-thresholding. Unlike the common applications in which AMP with hard-thresholding diverges, the properties of the THz channel favor this approach. It is shown that THz channel estimation via hard-thresholding AMP outperforms all previously proposed methods and approaches the oracle based performance closely.

Abstract-Terahertz image reconstruction based on compressed sensing and inverse Fresnel diffraction

Yingjie Shang, Xinke Wang, Wenfeng Sun, Peng Han, Jiasheng Ye, Shengfei Feng, and Yan Zhang

Fig. 1 (a) Schematic illustration of single-pixel THz imaging based on photoinduced dynamic masks. (b) Procedure of the proposed image reconstruction scheme. (c)-(h) give the simulation results, including (c) sample, (d) original THz temporal image, (e) THz diffraction image at temporal peak position, (f) THz temporal image recovered by CS, (g) THz spectral image at 0.3 THz, (h) THz image reconstructed by the IFD algorithm.

https://www.osapublishing.org/oe/abstract.cfm?uri=oe-27-10-14725

The introduction of compressed sensing (CS) effectively pushes the development of single-pixel THz imaging due to reducing the experimental time and avoiding raster scanning. In this work, a CS method based on photoinduced dynamic masks is employed to recover a THz diffraction field in the time domain, and an inverse Fresnel diffraction (IFD) integral is adopted to remove the influence of the diffraction and reconstruct the sharp THz spectral image in a single-pixel THz imaging system. The compatibility of the CS and IFD algorithms are validated on the simulation and experiment. Besides, the reconstruction effects are also systematically analyzed by reducing the measurement number and varying the diffraction distance, respectively. This work supplies a novel thinking for improving the practicability of single-pixel THz imaging.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Abstract-Reconstruction Methods in THz Single-pixel Imaging

Martin Burger, Janic Föcke, Lukas Nickel, Peter Jung, Sven Augustin

https://arxiv.org/abs/1903.08893

The aim of this paper is to discuss some advanced aspects of image reconstruction in single-pixel cameras, focusing in particular on detectors in the THz regime. We discuss the reconstruction problem from a computational imaging perspective and provide a comparison of the effects of several state-of-the art regularization techniques.
Moreover, we focus on some advanced aspects arising in practice with THz cameras, which lead to nonlinear reconstruction problems: the calibration of the beam reminiscent of the Retinex problem in imaging and phase recovery problems. Finally we provide an outlook to future challenges in the area.

A revolutionary imaging technique uses a single pixel to fill our terahertz blind spot

ORIGINAL IMAGE: RECONSTRUCTION METHODS IN THZ SINGLE-PIXEL IMAGING; EDITED BY MIT TECHNOLOGY REVIEW

https://www.technologyreview.com/s/613278/a-revolutionary-imaging-technique-uses-a-single-pixel-to-fill-our-terahertz-blind-spot/

Terahertz waves provide a unique view of the world but have always been hard to detect. That looks set to change.

At almost every wavelength engineers have electromagnetic
antennae that can detect and record the waves and create exotic images of the world at radio, microwave, infrared, visible, and x-ray frequencies.

But there is a blind spot in this spectrum. The technology is still in its infancy to detect radiation with a wavelength of between 1 and 0.3 millimeters and a frequency of about a terahertz. The equipment that can detect such radiation is bulky and expensive and the resulting images poor. Hence the “blind spot,” which engineers have called the terahertz gap.

A better way to capture these wavelengths is desperately needed, not least to gain a new window into the universe.

Today Martin Burger at the University of Munster in Germany and a few colleagues describe a revolutionary new imaging technique—compressed sensing—that is set to make this part of the electromagnetic spectrum more accessible. Applying the technique to terahertz waves is likely to change the way we see our world and the universe beyond.

First, some background. Terahertz waves pass through clothes but not through skin or metal. If your eyes could pick them up, people would appear naked but decorated with keys and coins but perhaps also knives and guns. So this kind of imaging has significant security applications, not to mention privacy implications.

Terahertz frequencies are difficult to detect because they sit on the electromagnetic spectrum between microwaves and infrared light, and there is an important difference between the way these types of radiation can be detected.

Microwaves, like radio waves, are made by accelerating a charge back and forth at the required frequency—in this case, up to about 300 gigahertz.  Detecting microwaves exploits the same process in reverse.

By contrast, infrared waves, like light, are made by making an electron in a suitable material jump between two electronic levels. This generates infrared light when the energy required to make the jump is equivalent to the energy of an infrared photon. The same process in reverse can also detect infrared photons.

Making and detecting terahertz waves is hard because they sit in the middle where neither technique works particularly well. It's tough to accelerate charges at terahertz frequencies. And materials with the required bandgap to create terahertz photons are difficult to find, and those that qualify often have to be cooled to cryogenic temperatures. That’s why terahertz detectors tend to be bulky, expensive, and hard to manage.

But compressed sensing can help, say Burger and co. In recent years, this technique has taken the world of imaging by storm because it allows a single pixel to record high-resolution images, even in 3-D.

The technique works by randomizing the reflected light from a scene and then recording it using a single pixel. The randomization can be done in various ways, but a common approach is to pass the light through a digital array called a spatial light modulator that displays a random pattern of transparent and opaque pixels. The randomization process is then repeated and the light field recorded again, and the entire process is repeated many times to generate many data points.

At first it’s hard to see how this can produce an image—after all, the light field is randomized. But the data points aren’t completely random. Indeed, each data point is correlated with all others because they all come from the same source—the original scene. So by finding this correlation, it is possible to recreate the original image.

It turns out that computer scientists have a variety of algorithms that can do this kind of number crunching. And the result is an image with a resolution that depends on the number of data points recorded by the pixel. The more data, the higher the resolution.

That has immediate application for terahertz imaging. Until now, the only way to create a 2-D image was to use an array of terahertz detectors or to scan a single detector back and forth to map out the light field. Neither technique is satisfactory because of the unwieldy size of terahertz detectors.

But compressed sensing offers an alternative: using a single terahertz detector to record multiple data points through a spatial light modulator that randomizes the terahertz light. That works well for visible and infrared light, and numerous groups have begun to exploit it successfully.

However, terahertz light introduces some additional complexities. For example, because terahertz waves are two or three orders of magnitude bigger than optical waves, they more easily diffract. This effect and others introduce distortions that make the image reconstruction much harder. It is this challenge of image reconstruction that Burger and co have taken on.

Their results are impressive. The team shows how various techniques can significantly improve the quality of resulting images. “The compressed-sensing approach based on single-pixel imaging has great potential to decrease measurement time and effort in THz imaging,” they say.

However, there are challenges ahead. One problem is in dealing with images made from more than one frequency of terahertz light. This kind of analysis is particularly important because it provides spectroscopic information about the chemical makeup of the subject in the image—for example, whether a crystalline powder is flour or some kind of drug. 

But this requires different types of mask. So a challenge is to find the best way to create a hyperspectral image using the smallest number of masks.

Nonetheless, Burger and co are optimistic that compressed sensing will allow rapid progress in finally closing the terahertz gap.

Ref: arxiv.org/abs/1903.08893 : Reconstruction Methods in THz Single-Pixel Imaging

Abstract-Semiconductor terahertz spatial modulators with high modulation depth and resolution for imaging applications

Tianlong Wen, Jing Tong, Dai-nan Zhang, Yunqiao Zhu, Qi-Ye Wen, Yuanpeng Li, Huai-Wu Zhang, Yu-Lan Jing,  Zhi-Yong Zhong

https://iopscience.iop.org/article/10.1088/1361-6463/ab146d/pdf

Spatial modulation of terahertz wave enabled by the charge carrier generation-recombination dynamics in semiconductor is promising for terahertz compressive sensing imaging since the modulation is broadband, low-loss and of enough speed (tens of thousands of Hertz). However their performance in terahertz compressive sensing imaging is significantly limited by their inferior modulation depth and resolution. Here silicon was cut into small pieces and packed closely in arrays to shut off the charge carrier diffusion between them and increase the resolution of the terahertz spatial modulator. A monolayer of gold nanoparticles was coated on the silicon surface to enhance the terahertz modulation depth through the enhanced generation of charge carriers by surface plasma. By comparison test, it is found that the gold nanoparticle coated small silicon arrays have improved contrast and resolution for terahertz imaging over the uncoated and coated large pieces of silicon respectively.

Abstract-Polarizer-free two-pixel polarimetric camera by compressive sensing

Julien Fade, Estéban Perrotin, and Jérôme Bobin

https://www.osapublishing.org/ao/abstract.cfm?uri=ao-57-7-B102&origin=search

We propose an original concept of compressive sensing (CS) polarimetric imaging based on a digital micromirror (DMD) array and two single-pixel detectors, without using any polarizer. The polarimetric sensitivity of the proposed setup is due to the tiny difference in Fresnel’s coefficients of reflecting mirrors, which is exploited here to form an original reconstruction problem including a CS problem and a source-separation task. We show that a two-step approach, tackling each problem successively, is outperformed by a dedicated combined reconstruction method, which is demonstrated in this paper and preferably implemented through a reweighted fast iterative shrinkage-thresholding algorithm. The combined reconstruction approach is then further improved by including physical constraints specific to the polarimetric imaging context considered, which are implemented in an original constrained generalized forward–backward algorithm. Numerical simulations demonstrate the efficiency of the two-pixel CS polarimetric imaging setup at retrieving polarimetric contrast data with significant compression rate and good reconstruction quality. The influence of experimental imperfections of the DMD is also analyzed through numerical simulations, and 2D polarimetric imaging reconstruction results are finally presented.

© 2018 Optical Society of America

Abstract-Compressed sensing with cyclic-S Hadamard matrix for terahertz imaging applications

Esra Şengün Ermeydan,  I. Cankaya,

https://www.researchgate.net/publication/322467886_Compressed_sensing_with_cyclic-S_Hadamard_matrix_for_terahertz_imaging_applications

Compressed Sensing (CS) with Cyclic-S Hadamard matrix is proposed for single pixel imaging applications in this study. In single pixel imaging scheme, N = r · c samples should be taken for r×c pixel image where · denotes multiplication. CS is a popular technique claiming that the sparse signals can be reconstructed with samples under Nyquist rate. Therefore to solve the slow data acquisition problem in Terahertz (THz) single pixel imaging, CS is a good candidate. However, changing mask for each measurement is a challenging problem since there is no commercial Spatial Light Modulators (SLM) for THz band yet, therefore circular masks are suggested so that for each measurement one or two column shifting will be enough to change the mask. The CS masks are designed using cyclic-S matrices based on Hadamard transform for 9 × 7 and 15 × 17 pixel images within the framework of this study. The %50 compressed images are reconstructed using total variation based TVAL3 algorithm. Matlab simulations demonstrates that cyclic-S matrices can be used for single pixel imaging based on CS. The circular masks have the advantage to reduce the mechanical SLMs to a single sliding strip, whereas the CS helps to reduce acquisition time and energy since it allows to reconstruct the image from fewer samples.

Abstract-Compressed sensing with near-field THz radiation

Rayko I. Stantchev, David B. Phillips, Peter Hobson, Samuel M. Hornett, Miles J. Padgett, and Euan Hendry

https://www.osapublishing.org/optica/abstract.cfm?uri=optica-4-8-989&origin=search

We demonstrate a form of near-field terahertz (THz) imaging that is compatible with compressed sensing algorithms. By spatially photomodulating THz pulses using a set of shaped binary optical patterns and employing a 6-μm-thick silicon wafer, we are able to reconstruct THz images of an object placed on the exit interface of the wafer. A single-element detector is used to measure the electric field amplitude of transmitted THz radiation for each projected pattern, with the ultra-thin wafer allowing us to access the THz evanescent near fields to achieve a spatial resolution of ∼9  μm$\sim 9\mathrm{\mu m}$ (𝜆/45$\lambda /45$ at 0.75 THz). We conclude by experimentally improving the image rate by a factor of ∼3$\sim 3$ by undersampling the object with adaptive and compressed sensing algorithms.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Abstract-Compressive correlation holography

Lorenzo Valzania, Peter Zolliker, and Erwin Hack
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-56-24-6949&origin=search

We propose and demonstrate a compressive sensing (CS) framework for correlation holography. This is accomplished by adopting the principle of compressive sensing and thresholding in the two-point intensity correlation. The measurement matrix and the sensing matrix that are required for applying the CS framework here are systematically extracted from the random illuminations of the laser speckle data. Reconstruction results using CS, CS with thresholding, and intensity correlation are compared. Our study reveals that liminal CS requires far fewer samples for the reconstruction of the hologram and has wide application in image reconstruction.

© 2017 Optical Society of America

Abstract-Compressive Sensing Imaging at Sub-THz Frequency in Transmission Mode

Vedat Ali Özkan, Yıldız Menteşe, Taylan Takan, Asaf Behzat Şahin, Hakan Altan

https://link.springer.com/chapter/10.1007/978-94-024-1093-8_7

Due to lack of widespread array imaging techniques in the THz range, point detector applications coupled with spatial modulation schemes are being investigated using compressive sensing (CS) techniques. CS algorithms coupled with innovative spatial modulation schemes which allow the control of pixels on the image plane from which the light is focused onto single pixel THz detector has been shown to rapidly generate images of objects. Using a CS algorithm, the image of an object can be reconstructed rapidly. Using a multiplied Schottky diode based multiplied millimeter wave source working at 113 GHz, a metal cutout letter F, which served as the target was illuminated in transmission. The image is spatially discretized by laser machined, 10 × 10 pixel metal apertures to demonstrate the technique of spatial modulation coupled with compressive sensing. The image was reconstructed by modulating the source and measuring the transmitted flux through the metal apertures using a Golay cell. Experimental results were compared to reference image to assess reconstruction performance using χ2 index. It is shown that a satisfactory image is reconstructed below the Nyquist rate which demonstrates that after taking into account the light intensity distribution at the image plane, compressive sensing is an advantageous method to be employed for remote sensing with point detectors.

Abstract-Compressive sensing resonator spectroscopy

Yaniv Oiknine, Isaac August, Dan G. Blumberg, and Adrian Stern

https://www.osapublishing.org/ol/abstract.cfm?uri=ol-42-1-25

We present a new fast compressive spectroscopic technique based on the resonance spectrometric mechanism. This technique uses an appropriately designed Fabry–Perot resonator and a photo-sensor in order to acquire different multiplexed spectral modulations, from which the original signal is reconstructed using a compressive sensing reconstruction algorithm. We present experimental results that demonstrate the acquisition of hundreds of spectral bands with a compression ratio of about 1:13.

© 2016 Optical Society of America

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Abstract-Full-Color Stereoscopic Imaging With a Single-Pixel Photodetector

Eva Salvador-Balaguer, Pere Clemente, Enrique Tajahuerce, Filiberto Pla, and Jesús Lancis

https://www.osapublishing.org/jdt/abstract.cfm?uri=jdt-12-4-417

We present an optical system for stereoscopic color imaging by using a single-pixel detector. The system works by illuminating the input scene with a sequence of microstructured light patterns generated by a color digital light projector (DLP). A single monochromatic photodiode, synchronized with the DLP, measures the light scattered by the object for each pattern. The image is recovered computationally by applying compressive sensing techniques. The RGB chromatic components of the image are discriminated by exploiting the time-multiplexed color codification of the DLP. The stereoscopic pair is obtained by splitting the light field generated by the DLP and projecting microstructured light patterns onto the sample from two different directions. The experimental setup is configured by simple optical components, a commercial photodiode and an off-the-shelf DLP projector. Color stereoscopic images of a 3-D scene obtained with this system are shown.

© 2015 IEEE

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Abstract-Compressive sensing for direct millimeter-wave holographic imaging

Compressive sensing for direct millimeter-wave holographic imaging Lingbo Qiao, Yingxin Wang, Zongjun Shen, Ziran Zhao, and Zhiqiang Chen  »View Author Affiliations

http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-54-11-3280

Applied Optics, Vol. 54, Issue 11, pp. 3280-3289 (2015)
http://dx.doi.org/10.1364/AO.54.003280

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Direct millimeter-wave (MMW) holographic imaging, which provides both the amplitude and phase information by using the heterodyne mixing technique, is considered a powerful tool for personnel security surveillance. However, MWW imaging systems usually suffer from the problem of high cost or relatively long data acquisition periods for array or single-pixel systems. In this paper, compressive sensing (CS), which aims at sparse sampling, is extended to direct MMW holographic imaging for reducing the number of antenna units or the data acquisition time. First, following the scalar diffraction theory, an exact derivation of the direct MMW holographic reconstruction is presented. Then, CS reconstruction strategies for complex-valued MMW images are introduced based on the derived reconstruction formula. To pursue the applicability for near-field MMW imaging and more complicated imaging targets, three sparsity bases, including total variance, wavelet, and curvelet, are evaluated for the CS reconstruction of MMW images. We also discuss different sampling patterns for single-pixel, linear array and two-dimensional array MMW imaging systems. Both simulations and experiments demonstrate the feasibility of recovering MMW images from measurements at 1/2 or even 1/4 of the Nyquist rate.

© 2015 Optical Society of America

Abstract-Compressed sensing of terahertz radar azimuth-elevation imaging

Hongqiang Wang, Ruijun Wang, Bin Deng, Wuge Su

National University of Defense Technology, College of Electronic Science and Engineering, No. 109, Deya Road, Changsha 410073, China

http://electronicimaging.spiedigitallibrary.org/article.aspx?articleid=2174076%20&journalid=94

J. Electron. Imaging. 24(1), 013035 (Feb 24, 2015). doi:10.1117/1.JEI.24.1.013035

There is increasing interest in high-resolution radar imaging of targets, and the recent development of terahertz (THz) imaging technique provides the depiction ability of targets in detail. The compressed sensing theory is introduced into terahertz radar azimuth-elevation imaging for facilitating the increasing sampling pressure and obtaining the improved imagery by exploiting the block sparse structure of a target’s reflectivity distribution. Compared with the conventional processing of even block partition in block sparsity, a block-coherence definition for uneven block partition is proposed as a sensing configuration quality parameter, and its relationship to the imagery reconstruction performance is verified. Further, a contrast metric for evaluating the improved image of uneven block partition is discussed without the knowledge of a true imaging result. The electromagnetic calculation data are used for the verification of imaging.

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10 Patents on Compressive Sensing Issued to InView Technology Corporation in 2014

http://inviewcorp.com/news/10-patents-on-compressive-sensing-issued-to-inview-technology-corporation-in-2014/#.VOvZj4ZHarU

And there are more on the way!

Ten patents were issued to InView Technology Corporation in 2014 covering the implementation and improvement of its Compressive Sensing camera architecture and algorithms.  With its initial product, the InView210™, InView has developed the world’s first SWIR camera based on the computational imaging architecture of compressive sensing.  InView continues to enhance its IP portfolio of 12 issued patents and 10 additional patent applications surrounding the implementation of its unique imaging modality, whose mathematical foundations were developed only within the last decade.  The foundational patent on the single-pixel camera architecture was issued in 2012 to Rice University and, along with other related patents, is exclusively licensed by InView.

Current development projects funded by DoD and NSF grants include a compressive video camera with high speed event detection capabilities.  InView is also developing a multi-spectral camera that can create false-color images combining visible and near infrared wavebands.

InView continues to innovate its compressive sensing architecture and data acquisition strategies to take advantage of its unique computational platform and welcomes licensing and investment inquiries.

Patents Issued in 2014

US 8,634,009 Dynamic range optimization in a compressive imaging system        January 21, 2014

Using differential detection methods and adjustable gain control to maximize the number of bits associated with the digitization of the compressive sensing measurement signal.

US 8,717,463 Adaptively filtering compressive imaging measurements to attenuate noise     May 6, 2014

Analog and digital filtering techniques applied to compressive sensing measurements to reduce zero-mean noise.

US 8,717,466 Dual-port measurements of light reflected from micromirror array              May 6, 2014

A unique way of making complementary measurements from the modulator used in the compressive camera architecture for inferring variations in light levels that contribute to noise

US 8,717,484 TIR prism to separate incident light and modulated light in compressive imaging device          May 6, 2014

Use of an optical prism device that allows the light path to and from the modulator to be made more compact contributing to a reduction in the size of the compressive camera and the use of standardized lenses.

US 8,717,492 Focusing mechanisms for compressive imaging device     May 6, 2014

The computational aspect of compressive sensing is used for the manual and automatic focusing of compressive sensing cameras.

US 8,717,551 Adaptive search for atypical regions in incident light field and spectral classification of light in the atypical regions            May 6, 2014

Algorithms and implementations are disclosed for detecting and classifying regions in the field of view of a compressive camera that are anomalous.

US 8,760,542 Compensation of compressive imaging measurements based on measurements from power meter   June 24, 2014

Using power meter measurements of calibration patterns and other techniques to significantly decrease noise levels in compressive sensing measurements and increasing image quality.

US 8,860,835 Decreasing image acquisition time for compressive imaging devices         October 14, 2014

Mechanisms are disclosed for speeding up the compressive sensing data acquisition process by dividing the field of view into multiple spatial regions, creating several data streams and using multiple detectors in parallel.

US 8,885,073 Dedicated power meter to measure background light level in compressive imaging system   November 11, 2014

Using the signal from a simple dedicated power meter to enhance compressive sensing imaging.

US 8,922,688 Hot spot correction in a compressive imaging system       December 30, 2014

Adaptive control of the modulator within the compressive camera architecture provides the means for automatically aggregating or removing regions in the field of view of a compressive camera that are excessively bright or otherwise of interest or not typical for the scene.

Patents Issued in 2013

US 8,570,406 Low pass filtering of compressive imaging measurements to infer light level variations           October 29, 2013

A method for compensating for background light level variations experienced during compressive measurement acquisition by low-pass filtering the measurements.

US 8, 570,405 Determining light level variation in compressive imaging by injecting calibration patterns into pattern sequence     October 29, 2013

A method for compensating for background light level variations experienced during compressive measurement acquisition using calibration patterns within the series of modulation patterns for compressive imaging.

Issued in 2012

US 8,199,244  Method and apparatus for compressive imaging device

InView has exclusive license for this foundational patent on the single-pixel camera architecture from Rice University.