Roy M. Matic

On generalized-marginal time-frequency distributions

We introduce a family of time-frequency (TF) distributions with generalized marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transforms of the signal. We present a necessary and sufficient condition for a TF distribution in Cohens class to satisfy generalized marginals. We then modify the existing well-known TF distributions in Cohens class, such as Choi-Williams (1989) and Page distributions, so that the modified ones have generalized marginals. Numerical examples are presented to show that the proposed TF distributions have the advantages of both Wigner-Ville and other quadratic TF distributions, which only have the conventional marginals. Moreover, they also indicate that the generalized-marginal TF distributions with proper marginals are more robust than the Wigner-Ville and the Choi-Williams distributions when signals contain additive noise.

Blazed phase liquid crystal beam steering

In this paper we describe a novel liquid crystal device for rapidly steering laser beams for high-power and large-aperture applications. The device consists of an array of optical phase modulators that contain a thin, active, liquid crystal layer sandwiched between two substrates. The unique aspect of the device is that each phase modulator can produce a linear (blazed) phase gradient, rather than the constant phase profile typical of other liquid crystal beam- steering devices. It is designed for use over a wide range of wavelengths and is particularly well suited for the deflection of short-wavelength laser beam. In this paper, we will describe device design, theoretical performance (diffraction efficiency and time response), and present experimental results of a device built to deflect a 1.064-micrometers laser beam.

An analog-to-information converter for wideband signals using a time encoding machine

The compressive sensing theory enables the analog-to-information conversion of a wideband signal directly by sampling the signal below the Nyquist rate and reconstruct the sampled signal perfectly. We developed a unique implementation of compressive sensing that is based on converting the signal to a time-encoded representation. The time encoding process converts an analog signal that has a continuous voltage range to a binary amplitude signal. In a time encoded signal representation, the important information is captured in the time points - the points where zero-crossing occur. This implementation is shown to be effective for signals sparse in frequency domain.

Generalized-marginal time-frequency distributions

We introduce a family of time-frequency (TF) distributions with generalized-marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transforms of the signal. We present a necessary and sufficient condition for a TF distribution in the Cohens class to satisfy generalized-marginals. We then modify the existing well-known TF distributions in the Cohens class, such as Choi-Williams, Page distributions, so that the modified ones have generalized marginals. Numerical examples are presented to show that the proposed TF distributions have the advantages of both Wigner-Ville and other quadratic TF distributions which only have the conventional marginals. Moreover, they also indicate that the generalized-marginal TF distributions with proper marginals are more robust than the Wigner-Ville and the Choi-Williams distributions when signals contain additive noise.

Performance limitations of compressive sensing for millimeter wave imaging

The authors present an analysis of compressive sensing (CS) as applied to millimeter wave and optical imaging systems, showing that the technique inherently reduces detection efficiency due to reflection and diffraction effects of the underlying electromagnetics. The results show that single-detector imaging approaches that rely on simultaneous detection of multiple spatial modes (i.e., image pixels) require an electrically large detector to maintain high detection efficiency.

Optimal pupil screen design for the estimation of partially coherent images

The effectiveness of optical preprocessing is examined for image-estimation applications. The problem is to design the pupil of the imaging system so that the detected image is the minimum-mean-square-error estimate of the desired image. The designs of several optimal pupil screens are presented. These designs demonstrate that both the optimum pupil screen and the effectiveness of optical preprocessing are functions of the statistics of the signal and the noise and of the coherence of the object illumination. The results indicate that preprocessing is more effective for coherent systems than for incoherent systems.

Accurate reconstruction of frequency-sparse signals from non-uniform samples

With the advent of a new sampling theory in recent years, compressed sensing (CS), it is possible to reconstruct signals from measurements far below the Nyquist rate. The CS theory assumes that signals are sparse and that measurement matrices satisfy certain conditions. Even though there have been many promising results, unfortunately there still exists a gap between the theory and actual real world applications. This is because of the fundamental problem that the CS formulation is discrete. We propose a sampling and reconstructing method for frequency-sparse signals that addresses this issue. The signals in our scenario are supported in a continuous sparsifying domain rather than discrete. This work focuses on a typical case in which the unknowns are frequencies and amplitudes. However, directly looking for the unknowns that best fit the measurements in the least-squares sense is a non-convex optimization problem, because sinusoids are oscillatory. Our approach extends the utility of CS to simplify this problem to a locally convex problem, hence making the solutions tractable. Direct measurements are taken from non-uniform time-samples, which is an extension of the CS problem with a subsampled Fourier matrix. The proposed reconstruction algorithm iteratively approximates the solutions using CS and then accurately solves for the frequencies with Newtons method and for the amplitudes with linear least squares solutions. Our simulations show success in accurate reconstruction of signals with arbitrary frequencies and significantly outperform current spectral compressed sensing methods in terms of reconstruction fidelity for both noise-free and noisy cases.

A Time-Encoding Machine Based High-Speed Analog-to-Digital Converter

A time-encoding machine (TEM) based new analog-to-digital converter (ADC) architecture is presented in this paper. The main advantage of this architecture is that it relies on asynchronous process and removes an important performance limiting factor in conventional ADCs: the clock jitter. Therefore, this architecture is suitable for very high speed ADCs. To expand the bandwidth coverage, the compressive sensing techniques is employed to reconstruct sparse signals with very high frequency. The system can run under two different modes: the normal mode where the signal is sampled at above Nyquist rate and the compressive sensing mode. Nonidealities in circuits and system parameter setting tradeoffs are analyzed to determine the best parameters for the system to reach optimal performance.

Neural networks for coefficient prediction in wavelet image coders

We present a unique method for estimating the upper frequency band coefficients solely from the low frequency information in a subband multiresolution decomposition. First, a Bayesian classifier predicts the significance or insignificance of the high frequency coefficients. A neural network then estimates the sign and magnitude of the visually significant information. This prediction model allows us to construct an image coder which can exclude transmission of the upper subbands and reconstruct this information at the decoder. We demonstrate results for a two level subband decomposition.

Comparison of optical predetection processing and postdetection linear processing for partially coherent image estimation

A comparison is made between the effectiveness of optical predetection processing and that of electronic postdetection filtering for image-estimation applications. The results indicate that optical preprocessing is more effective than postdetection filtering when the object illumination is coherent or nearly coherent, whereas the reverse is true for incoherent illumination. Two methods for using the processing capabilities of the optics in conjunction with the processing capabilities of the postdetection filter are also presented. The theory is formulated by assuming stationary statistics for the objects. Results of computer simulations performed on nonstationary objects indicate that the theory can be applied with minor modifications to nonstationary objects.