Signals In Fourier Domain Research Articles

Privacy Preserving Contraband Detection Using a Millimeter-Wave Dynamic Antenna Array

We present a privacy preserving technique for contraband detection using a real-time 75 GHz rotational dynamic antenna array that samples only a reduced set of Fourier-domain information to prevent image reconstruction of the screened subject. Complex objects such as handguns have sharp edges that correspond to sharp spatial frequency features in the Fourier domain. These features are dependent on the orientation of the object and manifest at millimeter-wave frequencies through conditions such as being concealed under clothing. The technique combines a dynamically rotated active interferometer and simple arithmetic feature extraction approach supporting a threshold-based classifier to identify when a handgun is concealed under clothing. The active interferometer technique utilizes noise transmitters to illuminate the test subject to produce thermal-like radiation, enabling Fourier-domain signal sampling, while the rotational dynamics support sampling that spans a circle in the 2-D Fourier domain to retrieve sharp-edge responses induced by concealed objects. We experimentally demonstrate the detection of concealed objects under clothing in a laboratory environment using a 75 GHz dynamic antenna array based on simple heuristic features extracted from statistics of the measured responses. The classifier is evaluated based on processing one or more subsequent measurements, showing a classification accuracy of 0.908 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F$</tex-math> </inline-formula> 1-score of 0.916 using four consecutive measurements.

Crosstalk-free volumetric in vivo imaging of a human retina with Fourier-domain full-field optical coherence tomography.

Fourier-domain full-field optical coherence tomography (FD-FF-OCT) is currently the fastest volumetric imaging technique that is able to generate a single 3-D volume of retina in less than 9 ms, corresponding to a voxel rate of 7.8 GHz. FD-FF-OCT is based on a fast camera, a rapidly tunable laser source, and Fourier-domain signal detection. However, crosstalk appearing due to multiply scattered light corrupts images with the speckle pattern, and therefore, lowers image quality. Here, for the first time, we report on a system that can acquire essentially crosstalk-free volumes of the retina by using a fast deformable membrane. It enables the visualization of choroids and a clear delineation of the retinal layers that is not possible with conventional FD-FF-OCT.

A new type of multilevel system for image sparse recovery

This work focuses on image sparse recovery problem. First, we construct a new kind of pseudo-directional multilevel system, which forms a tight frame in [Formula: see text]. Different from the widely used directional multilevel transforms curvelts and shearlets, whose subbands are neat and nonsensitive to the energy distribution of signals in Fourier domain, the proposed multilevel system is designed to have subbands with specific shape, the shape is oriented by the energy distribution. Thus, we can obtain more sparse structure of signals and low computation for the multilevel transform. Moreover, to detect directional singularities of signals effectively, a local directional gradient operator is introduced to catch the signal variation along different directions, it can be seen as the generalized gradient. Then we proposed a simple but efficient method for image sparse recovery, the split Bregman algorithm is employed to solve the proposed convex model which guarantees the global optimal solution. Some contrast experiments suggest that the sparse recovery by the proposed method performs well in artifacts’ suppressing and details’ extraction.

Grid-Free Localization Algorithm Using Low-rank Hankel Matrix for Super-Resolution Microscopy.

Localization microscopy, such as STORM / PALM, can reconstruct super-resolution images with a nanometer resolution through the iterative localization of fluorescence molecules. Recent studies in this area have focused mainly on the localization of densely activated molecules to improve temporal resolutions. However, higher density imaging requires an advanced algorithm that can resolve closely spaced molecules. Accordingly, sparsitydriven methods have been studied extensively. One of the major limitations of existing sparsity-driven approaches is the need for a fine sampling grid or for Taylor series approximation which may result in some degree of localization bias toward the grid. In addition, prior knowledge of the point-spread function (PSF) is required. To address these drawbacks, here we propose a true grid-free localization algorithm with adaptive PSF estimation. Specifically, based on the observation that sparsity in the spatial domain implies a low rank in the Fourier domain, the proposed method converts source localization problems into Fourier-domain signal processing problems so that a truly gridfree localization is possible. We verify the performance of the newly proposed method with several numerical simulations and a live-cell imaging experiment.

Laser Scanning Confocal Thermoreflectance Microscope for the Backside Thermal Imaging of Microelectronic Devices.

In this paper, we report on a confocal thermoreflectance imaging system that can examine the thermal characteristics of microelectronic devices by penetrating the backside of a device through the substrate. In this system, the local reflectivity variations due to heat generation in the device are measured point by point by a laser scanning confocal microscope capable of eliminating out-of-focus reflections and the thermoreflectance is extracted via Fourier-domain signal processing. In comparison to the conventional widefield thermoreflectance microscope, the proposed laser scanning confocal thermoreflectance microscope improves the thermoreflectance sensitivity by ~23 times and the spatial resolution by ~25% in backside thermoreflectance measurements.

Increased localization precision by interference fringe analysis.

We report a novel optical single-emitter-localization methodology that uses the phase induced by path length differences in a Mach-Zehnder interferometer to improve localization precision. Using information theory, we demonstrate that the localization capability of a modified Fourier domain signal generated by photon interference enables a more precise localization compared to a standard Gaussian intensity distribution of the corresponding point-spread function. The calculations were verified by numerical simulations and an exemplary experiment, where the centers of metal nanoparticles were localized to a precision of 3 nm.

Femtosecond pulse shaping enables detection of optical Kerr-effect (OKE) dynamics for molecular imaging.

We apply femtosecond pulse shaping to generate optical pulse trains that directly access a material's nonlinear refractive index (n2) and can thus determine time-resolved optical Kerr-effect (OKE) dynamics. Two types of static pulse trains are discussed: The first uses two identical fields delayed in time, plus a pump field at a different wavelength. Time-resolved OKE dynamics are retrieved by monitoring the phase of the interference pattern produced by the two identical fields in the Fourier-domain (FD) as a function of pump-probe-time-delay (where the probe is one of the two identical fields). The second pulse train uses three fields with equal time delays, but with the center field phase shifted by π/2. In this pulse scheme, changes on a sample's nonlinear refractive index produce a new frequency in the FD signal, which in turn yields background-free intensity changes in the conjugate (time) domain and provides superior signal-to-noise ratios. The demonstrated sensitivity improvements enable, for the first time to our knowledge, molecular imaging based on OKE dynamics.

Experimental Investigation on Correlation between Kansei Impression and Feature Quantity of Sound Signal in Fourier Domain

Experimental Investigation on Correlation between Kansei Impression and Feature Quantity of Sound Signal in Fourier Domain

Graph spectral image smoothing using the heat kernel

A new method for smoothing both gray-scale and color images is presented that relies on the heat diffusion equation on a graph. We represent the image pixel lattice using a weighted undirected graph. The edge weights of the graph are determined by the Gaussian weighted distances between local neighboring windows. We then compute the associated Laplacian matrix (the degree matrix minus the adjacency matrix). Anisotropic diffusion across this weighted graph-structure with time is captured by the heat equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigensystem with time. Image smoothing is accomplished by convolving the heat kernel with the image, and its numerical implementation is realized by using the Krylov subspace technique. The method has the effect of smoothing within regions, but does not blur region boundaries. We also demonstrate the relationship between our method, standard diffusion-based PDEs, Fourier domain signal processing and spectral clustering. Experiments and comparisons on standard images illustrate the effectiveness of the method.

Efficient computation of joint fractional Fourier domain signal representation

A joint fractional domain signal representation is proposed based on an intuitive understanding from a time-frequency distribution of signals that designates the joint time and frequency energy content. The joint fractional signal representation (JFSR) of a signal is so designed that its projections onto the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR, including its relations to quadratic time-frequency representations and fractional Fourier transformations, which include the oblique projections of the JFSR. We present a fast algorithm to compute radial slices of the JFSR and the results are shown for various signals at different fractionally ordered domains.