Event-triggered Sampling and Reconstruction of Sparse Real-valued Trigonometric Polynomials

We propose data acquisition from continuous-time signals belonging to the class of real-valued trigonometric polynomials using an event-triggered sampling paradigm. The sampling schemes proposed are: level crossing (LC), close to extrema LC, and extrema sampling. Analysis of robustness of these schemes to jitter, and bandpass additive gaussian noise is presented. In general these sampling schemes will result in non-uniformly spaced sample instants. We address the issue of signal reconstruction from the acquired data-set by imposing structure of sparsity on the signal model to circumvent the problem of gap and density constraints. The recovery performance is contrasted amongst the various schemes and with random sampling scheme. In the proposed approach, both sampling and reconstruction are non-linear operations, and in contrast to random sampling methodologies proposed in compressive sensing these techniques may be implemented in practice with low-power circuitry.

Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x- and y-coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.

Empirical Analysis of Sampling Based Estimators for Evaluating RBMs

The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is very difficult. In recent years some estimation methods are suggested for approximate computation of test log-likelihood. In this paper we present an empirical comparison of the main estimation methods, namely, the AIS algorithm for estimating the partition function, the CSL method for directly estimating the log-likelihood, and the RAISE algorithm that combines these two ideas.

Time-Instant Sampling Based Encoding of Time-Varying Acoustic Spectrum

The inner ear has been shown to characterize an acoustic stimuli by transducing fluid motion in the inner ear to mechanical bending of stereocilia on the inner hair cells (IHCs). The excitation motion/energy transferred to an IHC is dependent on the frequency spectrum of the acoustic stimuli, and the spatial location of the IHC along the length of the basilar membrane (BM). Subsequently, the afferent auditory nerve fiber (ANF) bundle samples the encoded waveform in the IHCs by synapsing with them. In this work we focus on sampling of information by afferent ANFs from the IHCs, and show computationally that sampling at specific time instants is sufficient for decoding of time-varying acoustic spectrum embedded in the acoustic stimuli. The approach is based on sampling the signal at its zero-crossings and higher-order derivative zero-crossings. We show results of the approach on time-varying acoustic spectrum estimation from cricket call signal recording. The framework gives a time-domain and non-spatial processing perspective to auditory signal processing. The approach works on the full band signal, and is devoid of modeling any bandpass filtering mimicking the BM action. Instead, we motivate the approach from the perspective of event-triggered sampling by afferent ANFs on the stimuli encoded in the IHCs. Though the approach gives acoustic spectrum estimation but it is shallow on its complete understanding for plausible bio-mechanical replication with current mammalian auditory mechanics insights.