5 research outputs found
Spatial Sound Localization via Multipath Euclidean Distance Matrix Recovery
A novel localization approach is proposed in order to find the position of an individual source using recordings of a single microphone in a reverberant enclosure. The multipath propagation is modeled by multiple virtual microphones as images of the actual single microphone and a multipath distance matrix is constructed whose components consist of the squared distances between the pairs of microphones (real or virtual) or the squared distances between the microphones and the source. The distances between the actual and virtual microphones are computed from the geometry of the enclosure. The microphone-source distances correspond to the support of the early reflections in the room impulse response associated with the source signal acquisition. The low-rank property of the Euclidean distance matrix is exploited to identify this correspondence. Source localization is achieved through optimizing the location of the source matching those measurements. The recording time of the microphone and generation of the source signal is asynchronous and estimated via the proposed procedure. Furthermore, a theoretically optimal joint localization and synchronization algorithm is derived by formulating the source localization as minimization of a quartic cost function. It is shown that the global minimum of the proposed cost function can be efficiently computed by converting it to a generalized trust region subproblem. Numerical simulations on synthetic data and real data recordings obtained by practical tests show the effectiveness of the proposed approach
-Analysis Minimization and Generalized (Co-)Sparsity: When Does Recovery Succeed?
This paper investigates the problem of signal estimation from undersampled
noisy sub-Gaussian measurements under the assumption of a cosparse model. Based
on generalized notions of sparsity, we derive novel recovery guarantees for the
-analysis basis pursuit, enabling highly accurate predictions of its
sample complexity. The corresponding bounds on the number of required
measurements do explicitly depend on the Gram matrix of the analysis operator
and therefore particularly account for its mutual coherence structure. Our
findings defy conventional wisdom which promotes the sparsity of analysis
coefficients as the crucial quantity to study. In fact, this common paradigm
breaks down completely in many situations of practical interest, for instance,
when applying a redundant (multilevel) frame as analysis prior. By extensive
numerical experiments, we demonstrate that, in contrast, our theoretical
sampling-rate bounds reliably capture the recovery capability of various
examples, such as redundant Haar wavelets systems, total variation, or random
frames. The proofs of our main results build upon recent achievements in the
convex geometry of data mining problems. More precisely, we establish a
sophisticated upper bound on the conic Gaussian mean width that is associated
with the underlying -analysis polytope. Due to a novel localization
argument, it turns out that the presented framework naturally extends to stable
recovery, allowing us to incorporate compressible coefficient sequences as
well
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
PHYSICS-DRIVEN STRUCTURED COSPARSE MODELING FOR SOURCE LOCALIZATION
Cosparse modeling is a recent alternative to sparse modeling, where the notion of dictionary is replaced by that of an analysis operator. When a known analysis operator is well adapted to describe the signals of interest, the model and associated algorithms can be used to solve inverse problems. Here we show how to derive an operator to model certain classes of signals that satisfy physical laws, such as the heat equation or the wave equation. We illustrate the approach on an acoustic inverse problem with a toy model of wave propagation and discuss its potential extensions and the challenges it raises