4,464 research outputs found
Matrix recovery using Split Bregman
In this paper we address the problem of recovering a matrix, with inherent
low rank structure, from its lower dimensional projections. This problem is
frequently encountered in wide range of areas including pattern recognition,
wireless sensor networks, control systems, recommender systems, image/video
reconstruction etc. Both in theory and practice, the most optimal way to solve
the low rank matrix recovery problem is via nuclear norm minimization. In this
paper, we propose a Split Bregman algorithm for nuclear norm minimization. The
use of Bregman technique improves the convergence speed of our algorithm and
gives a higher success rate. Also, the accuracy of reconstruction is much
better even for cases where small number of linear measurements are available.
Our claim is supported by empirical results obtained using our algorithm and
its comparison to other existing methods for matrix recovery. The algorithms
are compared on the basis of NMSE, execution time and success rate for varying
ranks and sampling ratios
A forward-backward view of some primal-dual optimization methods in image recovery
A wide array of image recovery problems can be abstracted into the problem of
minimizing a sum of composite convex functions in a Hilbert space. To solve
such problems, primal-dual proximal approaches have been developed which
provide efficient solutions to large-scale optimization problems. The objective
of this paper is to show that a number of existing algorithms can be derived
from a general form of the forward-backward algorithm applied in a suitable
product space. Our approach also allows us to develop useful extensions of
existing algorithms by introducing a variable metric. An illustration to image
restoration is provided
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