29,456 research outputs found
Blind Compressed Sensing Over a Structured Union of Subspaces
This paper addresses the problem of simultaneous signal recovery and
dictionary learning based on compressive measurements. Multiple signals are
analyzed jointly, with multiple sensing matrices, under the assumption that the
unknown signals come from a union of a small number of disjoint subspaces. This
problem is important, for instance, in image inpainting applications, in which
the multiple signals are constituted by (incomplete) image patches taken from
the overall image. This work extends standard dictionary learning and
block-sparse dictionary optimization, by considering compressive measurements,
e.g., incomplete data). Previous work on blind compressed sensing is also
generalized by using multiple sensing matrices and relaxing some of the
restrictions on the learned dictionary. Drawing on results developed in the
context of matrix completion, it is proven that both the dictionary and signals
can be recovered with high probability from compressed measurements. The
solution is unique up to block permutations and invertible linear
transformations of the dictionary atoms. The recovery is contingent on the
number of measurements per signal and the number of signals being sufficiently
large; bounds are derived for these quantities. In addition, this paper
presents a computationally practical algorithm that performs dictionary
learning and signal recovery, and establishes conditions for its convergence to
a local optimum. Experimental results for image inpainting demonstrate the
capabilities of the method
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
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