Ivan Dokmanić

Metals in proteins: correlation between the metal-ion type, coordination number and the amino-acid residues involved in the coordination

Metal ions are constituents of many metalloproteins, in which they have either catalytic (metalloenzymes) or structural functions. In this work, the characteristics of various metals were studied (Cu, Zn, Mg, Mn, Fe, Co, Ni, Cd and Ca in proteins with known crystal structure) as well as the specificity of their environments. The analysis was performed on two data sets: the set of protein structures in the Protein Data Bank (PDB) determined with resolution <1.5 A and the set of nonredundant protein structures from the PDB. The former was used to determine the distances between each metal ion and its electron donors and the latter was used to assess the preferred coordination numbers and common combinations of amino-acid residues in the neighbourhood of each metal. Although the metal ions considered predominantly had a valence of two, their preferred coordination number and the type of amino-acid residues that participate in the coordination differed significantly from one metal ion to the next. This study concentrates on finding the specificities of a metal-ion environment, namely the distribution of coordination numbers and the amino-acid residue types that frequently take part in coordination. Furthermore, the correlation between the coordination number and the occurrence of certain amino-acid residues (quartets and triplets) in a metal-ion coordination sphere was analysed. The results obtained are of particular value for the identification and modelling of metal-binding sites in protein structures derived by homology modelling. Knowledge of the geometry and characteristics of the metal-binding sites in metalloproteins of known function can help to more closely determine the biological activity of proteins of unknown function and to aid in design of proteins with specific affinity for certain metals.

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.

Can one hear the shape of a room: The 2-D polygonal case

We consider the problem of estimating room geometry from the acoustic room impulse response (RIR). Existing approaches addressing this problem exploit the knowledge of multiple RIRs. In contrast, we are interested in reconstructing the room geometry from a single RIR — a 1-D function of time. We discuss the uniqueness of the mapping between the geometry of a planar polygonal room and a single RIR. In addition to this theoretical analysis, we also propose an algorithm that performs the “blindfolded” room estimation. Furthermore, the derived results are used to construct an algorithm for localization in a known room using only a single RIR. Verification of the theoretical developments with numerical simulations is given before concluding the paper.

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.

Raking the Cocktail Party

We present the concept of an acoustic rake receiver-a microphone beamformer that uses echoes to improve the noise and interference suppression. The rake idea is well-known in wireless communications; it involves constructively combining different multipath components that arrive at the receiver antennas. Unlike spread-spectrum signals used in wireless communications, speech signals are not orthogonal to their shifts. Therefore, we focus on the spatial structure, rather than the temporal. Instead of explicitly estimating the channel, we create correspondences between early echoes in time and image sources in space. These multiple sources of the desired and the interfering signal offer additional spatial diversity that we can exploit in the beamformer design. We present several “intuitive” and optimal formulations of acoustic rake receivers, and show theoretically and numerically that the rake formulation of the maximum signal-to-interference-and-noise ratio beamformer offers significant performance boosts in terms of noise and interference suppression. Beyond signal-to-noise ratio, we observe gains in terms of the perceptual evaluation of speech quality (PESQ) metric for the speech quality. We accompany the paper by the complete simulation and processing chain written in Python. The code and the sound samples are available online at http://lcav.github.io/AcousticRake Receiver/.

Room helps: Acoustic localization with finite elements

Acoustic source localization often relies on the free-space/far-field model. Recent work exploiting spatio-temporal sparsity promises to go beyond these scenarios. However, it requires the knowledge of the transfer functions from each possible source location to each microphone. We propose a method for indoor acoustic source localization in which the physical modeling is implicit. By approximating the wave equation with the finite element method (FEM), we naturally get a sparse recovery formulation of the source localization. We demonstrate how exploiting the bandwidth leads to improved performance and surprising results, such as localization of multiple sources with one microphone, or hearing around corners. Numerical simulation results show the feasibility of such schemes.

Sensor networks for diffusion fields: Detection of sources in space and time

We consider the problem of reconstructing a diffusion field, such as temperature, from samples collected by a sensor network. Motivated by the fast decay of the eigenvalues of the diffusion equation, we approximate the field by a truncated series. We show that the approximation error decays rapidly with time. On the other hand, the information content in the field also decays with time, suggesting the need for a proper choice of the sampling strategy. We propose two algorithms for sampling and reconstruction of the field. The first one reconstructs the distribution of point sources appearing at known times using the finite rate of innovation (FRI) framework. The second algorithm addresses a more difficult problem of estimating the unknown times at which the point sources appear, in addition to their locations and magnitudes. It relies on the assumption that the sources appear at distinct times. We verify that the algorithms are capable of reconstructing the field accurately through a set of numerical experiments. Specifically, we show that the second algorithm successfully recovers an arbitrary number of sources with unknown release times, satisfying the assumption. For simplicity, we develop the 1-D theory, noting the possibility of extending the framework to more general domains.

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+√K)2 spatial samples. For large K, this sampling requirement improves over previously known FRI sampling schemes on the sphere by a factor of four. We showcase the versatility of the proposed algorithm by applying it to three 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.

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.

Source localization and tracking in non-convex rooms

We consider the estimation of the acoustic source position in a known room from recordings by a microphone array. We propose an algorithm that does not require the room to be convex, nor a line-of-sight path between the microphone array and the source to be present. Times of arrival of early echoes are exploited through the image source model, thereby transforming the indoor localization problem to a problem of localizing multiple sources in the free-field. The localized virtual sources are mirrored into the room using the image source method in the reverse direction. Further, we propose an optimization-based algorithm for improving the estimate of the source position. The algorithm minimizes a cost function derived from the geometry of the localization problem. We apply the designed optimization algorithm to track a moving source, and show through numerical simulations that it improves the tracking accuracy when compared with the naïve approach.