ELLIPSE FITTING USING FINITE RATE OF INNOVATION PRINCIPLES

We address the problem of parameter estimation of an ellipse from a limited number of samples. We develop a new approach for solving the ellipse fitting problem by showing that the x and y coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals. Uniform samples of x and y coordinate functions of the ellipse are modeled as a sum of weighted complex exponentials, for which we propose an efficient annihilating filter technique to estimate the ellipse parameters from the samples. The FRI framework allows for estimating the ellipse parameters reliably from partial or incomplete measurements even in the presence of noise. The efficiency and robustness of the proposed method is compared with state-of-art direct method. The experimental results show that the estimated parameters have lesser bias compared with the direct method and the estimation error is reduced by 5-10 dB relative to the direct method.

ON THE ROLE OF THE HILBERT TRANSFORM IN BOOSTING THE PERFORMANCE OF THE ANNIHILATING FILTER

We consider the problem of parameter estimation from real-valued multi-tone signals. Such problems arise frequently in spectral estimation. More recently, they have gained new importance in finite-rate-of-innovation signal sampling and reconstruction. The annihilating filter is a key tool for parameter estimation in these problems. The standard annihilating filter design has to be modified to result in accurate estimation when dealing with real sinusoids, particularly because the real-valued nature of the sinusoids must be factored into the annihilating filter design. We show that the constraint on the annihilating filter can be relaxed by making use of the Hilbert transform. We refer to this approach as the Hilbert annihilating filter approach. We show that accurate parameter estimation is possible by this approach. In the single-tone case, the mean-square error performance increases by 6 dB for signal-to-noise ratio (SNR) greater than 0 dB. We also present experimental results in the multi-tone case, which show that a significant improvement (about 6 dB) is obtained when the parameters are close to 0 or pi. In the mid-frequency range, the improvement is about 2 to 3 dB.

NESTED SPARSE BAYESIAN LEARNING FOR BLOCK-SPARSE SIGNALS WITH INTRA-BLOCK CORRELATION

In this work, we address the recovery of block sparse vectors with intra-block correlation, i.e., the recovery of vectors in which the correlated nonzero entries are constrained to lie in a few clusters, from noisy underdetermined linear measurements. Among Bayesian sparse recovery techniques, the cluster Sparse Bayesian Learning (SBL) is an efficient tool for block-sparse vector recovery, with intra-block correlation. However, this technique uses a heuristic method to estimate the intra-block correlation. In this paper, we propose the Nested SBL (NSBL) algorithm, which we derive using a novel Bayesian formulation that facilitates the use of the monotonically convergent nested Expectation Maximization (EM) and a Kalman filtering based learning framework. Unlike the cluster-SBL algorithm, this formulation leads to closed-form EMupdates for estimating the correlation coefficient. We demonstrate the efficacy of the proposed NSBL algorithm using Monte Carlo simulations.

AN OPTIMUM SHRINKAGE ESTIMATOR BASED ON MINIMUM-PROBABILITY-OF-ERROR CRITERION AND APPLICATION TO SIGNAL DENOISING

We address the problem of designing an optimal pointwise shrinkage estimator in the transform domain, based on the minimum probability of error (MPE) criterion. We assume an additive model for the noise corrupting the clean signal. The proposed formulation is general in the sense that it can handle various noise distributions. We consider various noise distributions (Gaussian, Student's-t, and Laplacian) and compare the denoising performance of the estimator obtained with the mean-squared error (MSE)-based estimators. The MSE optimization is carried out using an unbiased estimator of the MSE, namely Stein's Unbiased Risk Estimate (SURE). Experimental results show that the MPE estimator outperforms the SURE estimator in terms of SNR of the denoised output, for low (0 -10 dB) and medium values (10 - 20 dB) of the input SNR.

MAXIMUM A-POSTERIORI ESTIMATION OF MISSING SAMPLES WITH CONTINUITY CONSTRAINT IN ELECTROMAGNETIC ARTICULOGRAPHY DATA

Electromagnetic Articulography (EMA) technique is used to record the kinematics of different articulators while one speaks. EMA data often contains missing segments due to sensor failure. In this work, we propose a maximum a-posteriori (MAP) estimation with continuity constraint to recover the missing samples in the articulatory trajectories recorded using EMA. In this approach, we combine the benefits of statistical MAP estimation as well as the temporal continuity of the articulatory trajectories. Experiments on articulatory corpus using different missing segment durations show that the proposed continuity constraint results in a 30% reduction in average root mean squared error in estimation over statistical estimation of missing segments without any continuity constraint.

Is General Relativity a simplified theory?

IARD 8th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields - Galileo Galilei Inst Theoret Phys (GGI), Florence, ITALY - MAY 29-JUN 01, 2012. Edited by:Horowitz, LP