Reza Parhizkar

Acoustic echoes reveal room shape

Imagine that you are blindfolded inside an unknown room. You snap your fingers and listen to the room’s response. Can you hear the shape of the room? Some people can do it naturally, but can we design computer algorithms that hear rooms? We show how to compute the shape of a convex polyhedral room from its response to a known sound, recorded by a few microphones. Geometric relationships between the arrival times of echoes enable us to “blindfoldedly” estimate the room geometry. This is achieved by exploiting the properties of Euclidean distance matrices. Furthermore, we show that under mild conditions, first-order echoes provide a unique description of convex polyhedral rooms. Our algorithm starts from the recorded impulse responses and proceeds by learning the correct assignment of echoes to walls. In contrast to earlier methods, the proposed algorithm reconstructs the full 3D geometry of the room from a single sound emission, and with an arbitrary geometry of the microphone array. As long as the microphones can hear the echoes, we can position them as we want. Besides answering a basic question about the inverse problem of room acoustics, our results find applications in areas such as architectural acoustics, indoor localization, virtual reality, and audio forensics.

Euclidean Distance Matrices: Essential theory, algorithms, and applications

Euclidean distance matrices (EDMs) are matrices of the squared distances between points. The definition is deceivingly simple; thanks to their many useful properties, they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness, and show how the various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes, and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. The code for all of the described algorithms and to generate the figures in the article is available online at http://lcav.epfl.ch/ivan.dokmanic. Finally, we suggest directions for further research.

Sound speed estimation using wave-based ultrasound tomography: theory and GPU implementation

We present preliminary results obtained using a time domain wave-based reconstruction algorithm for an ultrasound transmission tomography scanner with a circular geometry. While a comprehensive description of this type of algorithm has already been given elsewhere, the focus of this work is on some practical issues arising with this approach. In fact, wave-based reconstruction methods suffer from two major drawbacks which limit their application in a practical setting: convergence is difficult to obtain and the computational cost is prohibitive. We address the first problem by appropriate initialization using a ray-based reconstruction. Then, the complexity of the method is reduced by means of an efficient parallel implementation on graphical processing units (GPU). We provide a mathematical derivation of the wave-based method under consideration, describe some details of our implementation and present simulation results obtained with a numerical phantom designed for a breast cancer detection application. The source code of our GPU implementation is freely available on the web at www.usense.org.

SINGLE-CHANNEL INDOOR MICROPHONE LOCALIZATION

We propose a novel method for single-channel microphone localization inside a known room. Unlike other approaches, we take advantage of the room reverberation, which enables us to use only a single fixed loudspeaker to localize the microphone. Our method uses an echo labeling approach that associates the echoes to the correct walls. Echo labeling leverages the properties of the Euclidean distance matrices formed from the distances between the virtual sources and the microphone. Experiments performed in a real lecture room verify the effectiveness of the proposed localization algorithm.

Ad hoc microphone array calibration

This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance matrix completion algorithm by alternative low-rank matrix completion and projection onto the Euclidean distance space. This approach confines the recovered matrix to the EDM cone at each iteration of the matrix completion algorithm. The theoretical guarantees of the calibration performance are obtained considering the random and locally structured missing entries as well as the measurement noise on the known distances. This study elucidates the links between the calibration error and the number of microphones along with the noise level and the ratio of missing distances. Thorough experiments on real data recordings and simulated setups are conducted to demonstrate these theoretical insights. A significant improvement is achieved by the proposed Euclidean distance matrix completion algorithm over the state-of-the-art techniques for ad hoc microphone array calibration. HighlightsEuclidean matrix completion enables calibration from partial distance measurements.A novel Euclidean matrix completion algorithm is proposed.The relation between error and number of microphones, noise and missing distances is derived.Theoretical insights are demonstrated by thorough experiments on real and simulated data.The performance is compared with SDP, S-Stress, MDS-MAP and Matrix completion.

Euclidean distance matrix completion for ad-hoc microphone array calibration

This paper addresses the application of missing data recovery via matrix completion for audio sensor networks. We propose a method based on Euclidean distance matrix completion for ad-hoc microphone array location calibration. This method can calibrate a full network from partial connectivity information. The pairwise distances of microphones in close proximity are estimated using the coherence model of the diffuse noise field. The distance matrix of the ad-hoc network is constructed where the distances of the microphones above a threshold are missing. We exploit the low-rank property of the squared distance matrix and apply a matrix completion method to recover the missing entries. In order to constrain the Euclidean space geometry, we propose the additional use of the Cadzow algorithm for matrix completion. The applicability of the proposed method is evaluated on real data recordings where a significant improvement over the state-of-the-art is achieved.

Calibration Using Matrix Completion With Application to Ultrasound Tomography

We study the application of matrix completion in the process of calibrating physical devices. In particular we propose an algorithm together with reconstruction bounds for calibrating circular ultrasound tomography devices. We use the time-of-flight (ToF) measurements between sensor pairs in a homogeneous medium to calibrate the system. The calibration process consists of a low-rank matrix completion algorithm to de-noise and estimate random and structured missing ToFs, and the classic multi-dimensional scaling method to estimate the sensor positions from the ToF measurements. We provide theoretical bounds on the calibration error. Several simulations are conducted to evaluate the theoretical results presented in this paper.

Calibration in circular ultrasound tomography devices

We consider the position calibration problem in circular tomography devices, where sensors deviate from a perfect circle. We introduce a new method of calibration based on the time-of-flight measurements between sensors when the enclosed medium is homogeneous. Bounds on the reconstruction errors are proven and results of simulations mimicking a scanning device are presented.

Sequences with minimal time-frequency spreads

For a given time or frequency spread, one can always find continuous-time signals, which achieve the Heisenberg uncertainty principle bound. This is known, however, not to be the case for discrete-time sequences; only widely spread sequences asymptotically achieve this bound. We provide a constructive method for designing sequences that are maximally compact in time for a given frequency spread. By formulating the problem as a semidefinite program, we show that maximally compact sequences do not achieve the classic Heisenberg bound. We further provide analytic lower bounds on the time-frequency spread of such signals.