Estimating Sparse Signals Using Integrated Wideband Dictionaries

In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard dictionary elements. Different from traditional dictionaries, the wideband dictionary allows for the use of dictionaries with fewer elements than the number of available samples without loss of resolution. The technique may be used on both one- and multi-dimensional signals, and may be exploited to refine several traditional sparse estimators, here illustrated with the LASSO and the SPICE estimators. Numerical examples illustrate the improved performance

Audio Inpainting

(c) 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Published version: IEEE Transactions on Audio, Speech and Language Processing 20(3): 922-932, Mar 2012. DOI: 10.1090/TASL.2011.2168211

TFAW: wavelet-based signal reconstruction to reduce photometric noise in time-domain surveys

There have been many efforts to correct systematic effects in astronomical light curves to improve the detection and characterization of planetary transits and astrophysical variability. Algorithms like the Trend Filtering Algorithm (TFA) use simultaneously-observed stars to remove systematic effects, and binning is used to reduce high-frequency random noise. We present TFAW, a wavelet-based modified version of TFA. TFAW aims to increase the periodic signal detection and to return a detrended and denoised signal without modifying its intrinsic characteristics. We modify TFA's frequency analysis step adding a Stationary Wavelet Transform filter to perform an initial noise and outlier removal and increase the detection of variable signals. A wavelet filter is added to TFA's signal reconstruction to perform an adaptive characterization of the noise- and trend-free signal and the noise contribution at each iteration while preserving astrophysical signals. We carried out tests over simulated sinusoidal and transit-like signals to assess the effectiveness of the method and applied TFAW to real light curves from TFRM. We also studied TFAW's application to simulated multiperiodic signals, improving their characterization. TFAW improves the signal detection rate by increasing the signal detection efficiency (SDE) up to a factor ~2.5x for low SNR light curves. For simulated transits, the transit detection rate improves by a factor ~2-5x in the low-SNR regime compared to TFA. TFAW signal approximation performs up to a factor ~2x better than bin averaging for planetary transits. The standard deviations of simulated and real TFAW light curves are ~40x better than TFA. TFAW yields better MCMC posterior distributions and returns lower uncertainties, less biased transit parameters and narrower (~10x) credibility intervals for simulated transits. We present a newly-discovered variable star from TFRM.Comment: Accepted for publication by A&A. 13 pages, 16 figures and 5 table

Accurate and robust spectral testing with relaxed instrumentation requirements

Spectral testing has been widely used to characterize the dynamic performances of the electrical signals and devices, such as Analog-to-Digital Converters (ADCs) for many decades. One of the difficulties faced is to accurately and cost-effectively test the continually higher performance devices. Standard test methods can be difficult to implement accurately and cost effectively, due to stringent requirements. To relax these necessary conditions and to reduce test costs, while achieving accurate spectral test results, several new algorithms are developed to perform accurate spectral and linearity test without requiring precise, expensive instruments. In this dissertation, three classes of methods for overcoming the above difficulties are presented. The first class of methods targeted the accurate, single-tone spectral testing. The first method targets the non-coherent sampling issue on spectral testing, especially when the non-coherently sampled signal has large distortions. The second method resolves simultaneous amplitude and frequency drift with non-coherent sampling. The third method achieves accurate linearity results for DAC-ADC co-testing, and generates high-purity sine wave using the nonlinear DAC in the system via pre-distortion. The fourth method targets ultra-pure sine wave generation with two nonlinear DACs, two simple filters, and a nonlinear ADC. These proposed methods are validated by both simulation and measurement results, and have demonstrated their high accuracy and robustness against various test conditions. The second class of methods deals with the accurate multi-tone spectral testing. The first method in this class resolves the non-coherent sampling issue in multi-tone spectral testing. The second method in this class introduces another proposed method to deal with multi-tone impure sources in spectral testing. The third method generates the multi-tone sine wave with minimum peak-to-average power ratio, which can be implemented in many applications, such as spectral testing and signal analysis. Similarly, simulation and measurement results validate the functionality and robustness of these proposed methods. Finally, the third class introduces two proposed methods to accurately test linearity characteristics of high-performance ADCs using low purity sinusoidal or ramp stimulus in the presence of flicker noise. Extensive simulation results have verified their effectiveness to reduce flicker noise influence and achieve accurate linearity results

Group Iterative Spectrum Thresholding for Super-Resolution Sparse Spectral Selection

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods break down in presence of high coherence and large noise. We propose a new regularization approach to handle model collinearity and obtain parsimonious frequency selection simultaneously. It takes advantage of the pairing structure of sine and cosine atoms in the frequency dictionary. A probabilistic spectrum screening is also developed for fast computation in high dimensions. A data-resampling version of high-dimensional Bayesian Information Criterion is used to determine the regularization parameters. Experiments show the efficacy and efficiency of the proposed algorithms in challenging situations with small sample size, high frequency resolution, and low signal-to-noise ratio

Spectral analysis for nonstationary audio

A new approach for the analysis of nonstationary signals is proposed, with a focus on audio applications. Following earlier contributions, nonstationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random signals. The focus is on time warping and amplitude modulation, and an approximate maximum-likelihood approach based on suitable approximations in the wavelet transform domain is developed. This paper provides theoretical analysis of the approximations, and introduces JEFAS, a corresponding estimation algorithm. The latter is tested and validated on synthetic as well as real audio signal.Comment: IEEE/ACM Transactions on Audio, Speech and Language Processing, Institute of Electrical and Electronics Engineers, In pres

Efficient detection and signal parameter estimation with application to high dynamic GPS receiver

In a system for deriving position, velocity, and acceleration information from a received signal emitted from an object to be tracked wherein the signal comprises a carrier signal phase modulated by unknown binary data and experiencing very high Doppler and Doppler rate, this invention provides combined estimation/detection apparatus for simultaneously detecting data bits and obtaining estimates of signal parameters such as carrier phase and frequency related to receiver dynamics in a sequential manner. There is a first stage for obtaining estimates of the signal parameters related to phase and frequency in the vicinity of possible data transitions on the basis of measurements obtained within a current data bit. A second stage uses the estimates from the first stage to decide whether or not a data transition has actually occurred. There is a third stage for removing data modulation from the received signal when a data transition has occurred and a fourth stage for using the received signal with data modulation removed therefrom to update global parameters which are dependent only upon receiver dynamics and independent of data modulation. Finally, there is a fifth stage for using the global parameters to determine the position, velocity, and acceleration of the object