1,556 research outputs found
An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]
This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. To make this possible, CS relies on two principles: sparsity, which pertains to the signals of interest, and incoherence, which pertains to the sensing modality.
Our intent in this article is to overview the basic CS theory that emerged in the works [1]–[3], present the key mathematical ideas underlying this theory, and survey a couple of important results in the field. Our goal is to explain CS as plainly as possible, and so our article is mainly of a tutorial nature. One of the charms of this theory is that it draws from various subdisciplines within the applied mathematical sciences, most notably probability theory. In this review, we have decided to highlight this aspect and especially the fact that randomness can — perhaps surprisingly — lead to very effective sensing mechanisms. We will also discuss significant implications, explain why CS is a concrete protocol for sensing and compressing data simultaneously (thus the name), and conclude our tour by reviewing important applications
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
Phase Harmonic Correlations and Convolutional Neural Networks
A major issue in harmonic analysis is to capture the phase dependence of
frequency representations, which carries important signal properties. It seems
that convolutional neural networks have found a way. Over time-series and
images, convolutional networks often learn a first layer of filters which are
well localized in the frequency domain, with different phases. We show that a
rectifier then acts as a filter on the phase of the resulting coefficients. It
computes signal descriptors which are local in space, frequency and phase. The
non-linear phase filter becomes a multiplicative operator over phase harmonics
computed with a Fourier transform along the phase. We prove that it defines a
bi-Lipschitz and invertible representation. The correlations of phase harmonics
coefficients characterise coherent structures from their phase dependence
across frequencies. For wavelet filters, we show numerically that signals
having sparse wavelet coefficients can be recovered from few phase harmonic
correlations, which provide a compressive representationComment: 26 pages, 8 figure
GPU-Accelerated Algorithms for Compressed Signals Recovery with Application to Astronomical Imagery Deblurring
Compressive sensing promises to enable bandwidth-efficient on-board
compression of astronomical data by lifting the encoding complexity from the
source to the receiver. The signal is recovered off-line, exploiting GPUs
parallel computation capabilities to speedup the reconstruction process.
However, inherent GPU hardware constraints limit the size of the recoverable
signal and the speedup practically achievable. In this work, we design parallel
algorithms that exploit the properties of circulant matrices for efficient
GPU-accelerated sparse signals recovery. Our approach reduces the memory
requirements, allowing us to recover very large signals with limited memory. In
addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc
parallelization of matrix-vector multiplications and matrix inversions.
Finally, we practically demonstrate our algorithms in a typical application of
circulant matrices: deblurring a sparse astronomical image in the compressed
domain
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