1,930 research outputs found
A fast sparse block circulant matrix vector product
In the context of computed tomography (CT), iterative image reconstruction techniques are gaining attention because high-quality images are becoming computationally feasible. They involve the solution of large systems of equations, whose cost is dominated by the sparse matrix vector product (SpMV). Our work considers the case of the sparse matrices being block circulant, which arises when taking advantage of the rotational symmetry in the tomographic system. Besides the straightforward storage saving, we exploit the circulant structure to rewrite the poor-performance SpMVs into a high-performance product between sparse and dense matrices. This paper describes the implementations developed for multi-core CPUs and GPUs, and presents experimental results with typical CT matrices. The presented approach is up to ten times faster than without exploiting the circulant structure.Romero Alcalde, E.; Tomás Domínguez, AE.; Soriano Asensi, A.; Blanquer Espert, I. (2014). 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Convolutional Dictionary Learning through Tensor Factorization
Tensor methods have emerged as a powerful paradigm for consistent learning of
many latent variable models such as topic models, independent component
analysis and dictionary learning. Model parameters are estimated via CP
decomposition of the observed higher order input moments. However, in many
domains, additional invariances such as shift invariances exist, enforced via
models such as convolutional dictionary learning. In this paper, we develop
novel tensor decomposition algorithms for parameter estimation of convolutional
models. Our algorithm is based on the popular alternating least squares method,
but with efficient projections onto the space of stacked circulant matrices.
Our method is embarrassingly parallel and consists of simple operations such as
fast Fourier transforms and matrix multiplications. Our algorithm converges to
the dictionary much faster and more accurately compared to the alternating
minimization over filters and activation maps
Modulated Unit-Norm Tight Frames for Compressed Sensing
In this paper, we propose a compressed sensing (CS) framework that consists
of three parts: a unit-norm tight frame (UTF), a random diagonal matrix and a
column-wise orthonormal matrix. We prove that this structure satisfies the
restricted isometry property (RIP) with high probability if the number of
measurements for -sparse signals of length
and if the column-wise orthonormal matrix is bounded. Some existing structured
sensing models can be studied under this framework, which then gives tighter
bounds on the required number of measurements to satisfy the RIP. More
importantly, we propose several structured sensing models by appealing to this
unified framework, such as a general sensing model with arbitrary/determinisic
subsamplers, a fast and efficient block compressed sensing scheme, and
structured sensing matrices with deterministic phase modulations, all of which
can lead to improvements on practical applications. In particular, one of the
constructions is applied to simplify the transceiver design of CS-based channel
estimation for orthogonal frequency division multiplexing (OFDM) systems.Comment: submitted to IEEE Transactions on Signal Processin
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