Sampling Spherical Finite Rate of Innovation Signals

Sampling schemes on the sphere require O(L^2) samples to perfectly sample and reconstruct a signal with bandwidth L. If the signal in question is a low-pass observation of a finite collection of spikes or rotations of a known function, we can use less samples. We propose an algorithm that improves over the best known finite rate of innovation (FRI) sampling scheme on the sphere by a factor of approximately four. Further, we show how multiple sound source localization (SSL) by a spherical microphone array can be transformed into a spherical FRI sampling problem. We certify the effectiveness of the proposed algorithm by using it to solve the SSL problem

Sampling and Exact Reconstruction of Pulses with Variable Width

Recent sampling results enable the reconstruction of signals composed of streams of fixed-shaped pulses. These results have found applications in topics as varied as channel estimation, biomedical imaging and radio astronomy. However, in many real signals, the pulse shapes vary throughout the signal. In this paper, we show how to sample and perfectly reconstruct Lorentzian pulses with variable width. Since a stream of Lorentzian pulses has a finite number of degrees of freedom per unit time, it belongs to the class of signals with finite rate of innovation (FRI). In the noiseless case, perfect recovery is guaranteed by a set of theorems. In addition, we verify that our algorithm is robust to model-mismatch and noise. This allows us to apply the technique to two practical applications: electrocardiogram (ECG) compression and bidirectional reflectance distribution function (BRDF) sampling. ECG signals are one dimensional, but the BRDF is a higher dimensional signal, which is more naturally expressed in a spherical coordinate system; this motivated us to extend the theory to the 2D and spherical cases. Experiments on real data demonstrate the viability of the proposed model for ECG acquisition and compression, as well as the efficient representation and low-rate sampling of specular BRDFs

Sampling Sparse Signals on the Sphere: Algorithms and Applications

We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations. Central to our algorithm is a generalization of the annihilating filter method, a tool widely used in array signal processing and finite-rate-of-innovation (FRI) sampling. The proposed algorithm can reconstruct $K$ spikes from $(K+\sqrt{K})^2$ spatial samples. This sampling requirement improves over previously known FRI sampling schemes on the sphere by a factor of four for large $K$. We showcase the versatility of the proposed algorithm by applying it to three different problems: 1) sampling diffusion processes induced by localized sources on the sphere, 2) shot noise removal, and 3) sound source localization (SSL) by a spherical microphone array. In particular, we show how SSL can be reformulated as a spherical sparse sampling problem.Comment: 14 pages, 8 figures, submitted to IEEE Transactions on Signal Processin

Sparse image reconstruction on the sphere: analysis and synthesis

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems, and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the l1 norm appearing in the regularisation problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353 GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.Comment: 11 pages, 6 Figure

FRIDA: FRI-Based DOA Estimation for Arbitrary Array Layouts

In this paper we present FRIDA---an algorithm for estimating directions of arrival of multiple wideband sound sources. FRIDA combines multi-band information coherently and achieves state-of-the-art resolution at extremely low signal-to-noise ratios. It works for arbitrary array layouts, but unlike the various steered response power and subspace methods, it does not require a grid search. FRIDA leverages recent advances in sampling signals with a finite rate of innovation. It is based on the insight that for any array layout, the entries of the spatial covariance matrix can be linearly transformed into a uniformly sampled sum of sinusoids.Comment: Submitted to ICASSP201

Virtual sensors for local, three dimensional, broadband multiple-channel active noise control and the effects on the quiet zones

In this paper, two state of the art virtual sensor algorithms, i.e. the Remote Microphone Technique (RMT) and the Kalman filter based Virtual Sensing algorithm (KVS) are compared, in both state space (SS) and finite impulse response (FIR) implementations. The comparison focuses on the accuracy of the estimated sound pressure signals at the virtual locations and is based on actual measurements in a practical situation. The FIR implementation of the RMT algorithm was found to produce the most reliable results. It is implemented in a local, three dimensional, real-time, multiple-channel, broadband active noise control system. With this implementation, the benefits and limitations of the RMT-ANC system on the shape and size of the quiet zones are investigated

Bearing-only acoustic tracking of moving speakers for robot audition

This paper focuses on speaker tracking in robot audition for human-robot interaction. Using only acoustic signals, speaker tracking in enclosed spaces is subject to missing detections and spurious clutter measurements due to speech inactivity, reverberation and interference. Furthermore, many acoustic localization approaches estimate speaker direction, hence providing bearing-only measurements without range information. This paper presents a probability hypothesis density (PHD) tracker that augments the bearing-only speaker directions of arrival with a cloud of range hypotheses at speaker initiation and propagates the random variates through time. Furthermore, due to their formulation PHD filters explicitly model, and hence provide robustness against, clutter and missing detections. The approach is verified using experimental results