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We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off- diagonal blocks. This comprises probl ...
Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...
We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off-diagonal blocks. This comprises proble ...
We study the problem of learning constitutive features for the effective representation of graph signals, which can be considered as observations collected on different graph topologies. We propose to learn graph atoms and build graph dictionaries that pro ...
2015
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We develop an efficient learning framework to construct signal dictionaries for sparse representation by selecting the dictionary columns from multiple candidate bases. By sparse, we mean that only a few dictionary elements, compared to the ambient signal ...
2011
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This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via ℓ1-minimisation. The problem can also be seen as factorising a \ddim×\nsig matrix $Y=(y_1 \ldots y_\nsig), , y_n\in \R^\ ...
Institute of Electrical and Electronics Engineers2010
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This paper introduces a novel algorithm for sparse approximation in redundant dictionaries called the M-term pursuit (MTP). This algorithm decomposes a signal into a linear combination of atoms that are selected in order to represent the main signal compon ...
Institute of Electrical and Electronics Engineers2012
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Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution of the image reconstruction problem. An alternative to DAS consists in using iterative techniques which require both an a ...
2017
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This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...
Compressed sensing is a new trend in signal processing for efficient sampling and signal acquisition. The idea is that most real-world signals have a sparse representation in an appropriate basis and this can be exploited to capture the sparse signal by ta ...
