381 research outputs found
Designing Gabor windows using convex optimization
Redundant Gabor frames admit an infinite number of dual frames, yet only the
canonical dual Gabor system, constructed from the minimal l2-norm dual window,
is widely used. This window function however, might lack desirable properties,
e.g. good time-frequency concentration, small support or smoothness. We employ
convex optimization methods to design dual windows satisfying the Wexler-Raz
equations and optimizing various constraints. Numerical experiments suggest
that alternate dual windows with considerably improved features can be found
Reconstruction de phase et de signaux audio avec des fonctions de coût non-quadratiques
Audio signal reconstruction consists in recovering sound signals from incomplete or degraded representations. This problem can be cast as an inverse problem. Such problems are frequently tackled with the help of optimization or machine learning strategies. In this thesis, we propose to change the cost function in inverse problems related to audio signal reconstruction. We mainly address the phase retrieval problem, which is common when manipulating audio spectrograms. A first line of work tackles the optimization of non-quadratic cost functions for phase retrieval. We study this problem in two contexts: audio signal reconstruction from a single spectrogram and source separation. We introduce a novel formulation of the problem with Bregman divergences, as well as algorithms for its resolution. A second line of work proposes to learn the cost function from a given dataset. This is done under the framework of unfolded neural networks, which are derived from iterative algorithms. We introduce a neural network based on the unfolding of the Alternating Direction Method of Multipliers, that includes learnable activation functions. We expose the relation between the learning of its parameters and the learning of the cost function for phase retrieval. We conduct numerical experiments for each of the proposed methods to evaluate their performance and their potential with audio signal reconstruction
DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds
We present a new deep unfolding network for analysis-sparsity-based
Compressed Sensing. The proposed network coined Decoding Network (DECONET)
jointly learns a decoder that reconstructs vectors from their incomplete, noisy
measurements and a redundant sparsifying analysis operator, which is shared
across the layers of DECONET. Moreover, we formulate the hypothesis class of
DECONET and estimate its associated Rademacher complexity. Then, we use this
estimate to deliver meaningful upper bounds for the generalization error of
DECONET. Finally, the validity of our theoretical results is assessed and
comparisons to state-of-the-art unfolding networks are made, on both synthetic
and real-world datasets. Experimental results indicate that our proposed
network outperforms the baselines, consistently for all datasets, and its
behaviour complies with our theoretical findings.Comment: Accepted in IEEE Transactions on Signal Processin
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