A Few Photons Among Many: Unmixing Signal and Noise for Photon-Efficient Active Imaging

Conventional LIDAR systems require hundreds or thousands of photon detections to form accurate depth and reflectivity images. Recent photon-efficient computational imaging methods are remarkably effective with only 1.0 to 3.0 detected photons per pixel, but they are not demonstrated at signal-to-background ratio (SBR) below 1.0 because their imaging accuracies degrade significantly in the presence of high background noise. We introduce a new approach to depth and reflectivity estimation that focuses on unmixing contributions from signal and noise sources. At each pixel in an image, short-duration range gates are adaptively determined and applied to remove detections likely to be due to noise. For pixels with too few detections to perform this censoring accurately, we borrow data from neighboring pixels to improve depth estimates, where the neighborhood formation is also adaptive to scene content. Algorithm performance is demonstrated on experimental data at varying levels of noise. Results show improved performance of both reflectivity and depth estimates over state-of-the-art methods, especially at low signal-to-background ratios. In particular, accurate imaging is demonstrated with SBR as low as 0.04. This validation of a photon-efficient, noise-tolerant method demonstrates the viability of rapid, long-range, and low-power LIDAR imaging

Multiscale Bayesian State Space Model for Granger Causality Analysis of Brain Signal

Modelling time-varying and frequency-specific relationships between two brain signals is becoming an essential methodological tool to answer heoretical questions in experimental neuroscience. In this article, we propose to estimate a frequency Granger causality statistic that may vary in time in order to evaluate the functional connections between two brain regions during a task. We use for that purpose an adaptive Kalman filter type of estimator of a linear Gaussian vector autoregressive model with coefficients evolving over time. The estimation procedure is achieved through variational Bayesian approximation and is extended for multiple trials. This Bayesian State Space (BSS) model provides a dynamical Granger-causality statistic that is quite natural. We propose to extend the BSS model to include the \`{a} trous Haar decomposition. This wavelet-based forecasting method is based on a multiscale resolution decomposition of the signal using the redundant \`{a} trous wavelet transform and allows us to capture short- and long-range dependencies between signals. Equally importantly it allows us to derive the desired dynamical and frequency-specific Granger-causality statistic. The application of these models to intracranial local field potential data recorded during a psychological experimental task shows the complex frequency based cross-talk between amygdala and medial orbito-frontal cortex. Keywords: \`{a} trous Haar wavelets; Multiple trials; Neuroscience data; Nonstationarity; Time-frequency; Variational methods The published version of this article is Cekic, S., Grandjean, D., Renaud, O. (2018). Multiscale Bayesian state-space model for Granger causality analysis of brain signal. Journal of Applied Statistics. https://doi.org/10.1080/02664763.2018.145581

A modulation property of time-frequency derivatives of filtered phase and its application to aperiodicity and fo estimation

We introduce a simple and linear SNR (strictly speaking, periodic to random power ratio) estimator (0dB to 80dB without additional calibration/linearization) for providing reliable descriptions of aperiodicity in speech corpus. The main idea of this method is to estimate the background random noise level without directly extracting the background noise. The proposed method is applicable to a wide variety of time windowing functions with very low sidelobe levels. The estimate combines the frequency derivative and the time-frequency derivative of the mapping from filter center frequency to the output instantaneous frequency. This procedure can replace the periodicity detection and aperiodicity estimation subsystems of recently introduced open source vocoder, YANG vocoder. Source code of MATLAB implementation of this method will also be open sourced.Comment: 8 pages 9 figures, Submitted and accepted in Interspeech201

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation

A Robust Zero-point Attraction LMS Algorithm on Near Sparse System Identification

The newly proposed $l_1$ norm constraint zero-point attraction Least Mean Square algorithm (ZA-LMS) demonstrates excellent performance on exact sparse system identification. However, ZA-LMS has less advantage against standard LMS when the system is near sparse. Thus, in this paper, firstly the near sparse system modeling by Generalized Gaussian Distribution is recommended, where the sparsity is defined accordingly. Secondly, two modifications to the ZA-LMS algorithm have been made. The $l_1$ norm penalty is replaced by a partial $l_1$ norm in the cost function, enhancing robustness without increasing the computational complexity. Moreover, the zero-point attraction item is weighted by the magnitude of estimation error which adjusts the zero-point attraction force dynamically. By combining the two improvements, Dynamic Windowing ZA-LMS (DWZA-LMS) algorithm is further proposed, which shows better performance on near sparse system identification. In addition, the mean square performance of DWZA-LMS algorithm is analyzed. Finally, computer simulations demonstrate the effectiveness of the proposed algorithm and verify the result of theoretical analysis.Comment: 20 pages, 11 figure