103 research outputs found
Discrete Signal Reconstruction by Sum of Absolute Values
In this letter, we consider a problem of reconstructing an unknown discrete
signal taking values in a finite alphabet from incomplete linear measurements.
The difficulty of this problem is that the computational complexity of the
reconstruction is exponential as it is. To overcome this difficulty, we extend
the idea of compressed sensing, and propose to solve the problem by minimizing
the sum of weighted absolute values. We assume that the probability
distribution defined on an alphabet is known, and formulate the reconstruction
problem as linear programming. Examples are shown to illustrate that the
proposed method is effective.Comment: IEEE Signal Processing Letters (to appear
L1 Control Theoretic Smoothing Splines
In this paper, we propose control theoretic smoothing splines with L1
optimality for reducing the number of parameters that describes the fitted
curve as well as removing outlier data. A control theoretic spline is a
smoothing spline that is generated as an output of a given linear dynamical
system. Conventional design requires exactly the same number of base functions
as given data, and the result is not robust against outliers. To solve these
problems, we propose to use L1 optimality, that is, we use the L1 norm for the
regularization term and/or the empirical risk term. The optimization is
described by a convex optimization, which can be efficiently solved via a
numerical optimization software. A numerical example shows the effectiveness of
the proposed method.Comment: Accepted for publication in IEEE Signal Processing Letters. 4 pages
(twocolumn), 5 figure
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