123,615 research outputs found
Subspace Methods for Joint Sparse Recovery
We propose robust and efficient algorithms for the joint sparse recovery
problem in compressed sensing, which simultaneously recover the supports of
jointly sparse signals from their multiple measurement vectors obtained through
a common sensing matrix. In a favorable situation, the unknown matrix, which
consists of the jointly sparse signals, has linearly independent nonzero rows.
In this case, the MUSIC (MUltiple SIgnal Classification) algorithm, originally
proposed by Schmidt for the direction of arrival problem in sensor array
processing and later proposed and analyzed for joint sparse recovery by Feng
and Bresler, provides a guarantee with the minimum number of measurements. We
focus instead on the unfavorable but practically significant case of
rank-defect or ill-conditioning. This situation arises with limited number of
measurement vectors, or with highly correlated signal components. In this case
MUSIC fails, and in practice none of the existing methods can consistently
approach the fundamental limit. We propose subspace-augmented MUSIC (SA-MUSIC),
which improves on MUSIC so that the support is reliably recovered under such
unfavorable conditions. Combined with subspace-based greedy algorithms also
proposed and analyzed in this paper, SA-MUSIC provides a computationally
efficient algorithm with a performance guarantee. The performance guarantees
are given in terms of a version of restricted isometry property. In particular,
we also present a non-asymptotic perturbation analysis of the signal subspace
estimation that has been missing in the previous study of MUSIC.Comment: submitted to IEEE transactions on Information Theory, revised versio
High-resolution sinusoidal analysis for resolving harmonic collisions in music audio signal processing
Many music signals can largely be considered an additive combination of
multiple sources, such as musical instruments or voice. If the musical sources
are pitched instruments, the spectra they produce are predominantly harmonic,
and are thus well suited to an additive sinusoidal model. However,
due to resolution limits inherent in time-frequency analyses, when the harmonics
of multiple sources occupy equivalent time-frequency regions, their
individual properties are additively combined in the time-frequency representation
of the mixed signal. Any such time-frequency point in a mixture
where multiple harmonics overlap produces a single observation from which
the contributions owed to each of the individual harmonics cannot be trivially
deduced. These overlaps are referred to as overlapping partials or harmonic
collisions. If one wishes to infer some information about individual sources in
music mixtures, the information carried in regions where collided harmonics
exist becomes unreliable due to interference from other sources. This interference
has ramifications in a variety of music signal processing applications
such as multiple fundamental frequency estimation, source separation, and
instrumentation identification.
This thesis addresses harmonic collisions in music signal processing applications.
As a solution to the harmonic collision problem, a class of signal
subspace-based high-resolution sinusoidal parameter estimators is explored.
Specifically, the direct matrix pencil method, or equivalently, the Estimation
of Signal Parameters via Rotational Invariance Techniques (ESPRIT)
method, is used with the goal of producing estimates of the salient parameters
of individual harmonics that occupy equivalent time-frequency regions. This
estimation method is adapted here to be applicable to time-varying signals
such as musical audio. While high-resolution methods have been previously
explored in the context of music signal processing, previous work has not
addressed whether or not such methods truly produce high-resolution sinusoidal parameter estimates in real-world music audio signals. Therefore, this
thesis answers the question of whether high-resolution sinusoidal parameter
estimators are really high-resolution for real music signals.
This work directly explores the capabilities of this form of sinusoidal parameter
estimation to resolve collided harmonics. The capabilities of this
analysis method are also explored in the context of music signal processing
applications. Potential benefits of high-resolution sinusoidal analysis are
examined in experiments involving multiple fundamental frequency estimation
and audio source separation. This work shows that there are indeed
benefits to high-resolution sinusoidal analysis in music signal processing applications,
especially when compared to methods that produce sinusoidal
parameter estimates based on more traditional time-frequency representations.
The benefits of this form of sinusoidal analysis are made most evident
in multiple fundamental frequency estimation applications, where substantial
performance gains are seen. High-resolution analysis in the context of
computational auditory scene analysis-based source separation shows similar
performance to existing comparable methods
Fusion of Multimodal Information in Music Content Analysis
Music is often processed through its acoustic realization. This is restrictive in the sense that music is clearly a highly multimodal concept where various types of heterogeneous information can be associated to a given piece of music (a musical score, musicians\u27 gestures, lyrics, user-generated metadata, etc.). This has recently led researchers to apprehend music through its various facets, giving rise to "multimodal music analysis" studies. This article gives a synthetic overview of methods that have been successfully employed in multimodal signal analysis. In particular, their use in music content processing is discussed in more details through five case studies that highlight different multimodal integration techniques. The case studies include an example of cross-modal correlation for music video analysis, an audiovisual drum transcription system, a description of the concept of informed source separation, a discussion of multimodal dance-scene analysis, and an example of user-interactive music analysis. In the light of these case studies, some perspectives of multimodality in music processing are finally suggested
On the Application of Generic Summarization Algorithms to Music
Several generic summarization algorithms were developed in the past and
successfully applied in fields such as text and speech summarization. In this
paper, we review and apply these algorithms to music. To evaluate this
summarization's performance, we adopt an extrinsic approach: we compare a Fado
Genre Classifier's performance using truncated contiguous clips against the
summaries extracted with those algorithms on 2 different datasets. We show that
Maximal Marginal Relevance (MMR), LexRank and Latent Semantic Analysis (LSA)
all improve classification performance in both datasets used for testing.Comment: 12 pages, 1 table; Submitted to IEEE Signal Processing Letter
An Introduction to Fourier Analysis with Applications to Music
In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for the mathematics utilized in digital signal processing
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