243,082 research outputs found
Verifiable conditions of -recovery of sparse signals with sign restrictions
We propose necessary and sufficient conditions for a sensing matrix to be
"s-semigood" -- to allow for exact -recovery of sparse signals with at
most nonzero entries under sign restrictions on part of the entries. We
express the error bounds for imperfect -recovery in terms of the
characteristics underlying these conditions. Furthermore, we demonstrate that
these characteristics, although difficult to evaluate, lead to verifiable
sufficient conditions for exact sparse -recovery and to efficiently
computable upper bounds on those for which a given sensing matrix is
-semigood. We concentrate on the properties of proposed verifiable
sufficient conditions of -semigoodness and describe their limits of
performance
Second-order sufficient conditions for error bounds in banach spaces
10.1137/040621661SIAM Journal on Optimization173795-80
Nonlocal error bounds for piecewise affine functions
The paper is devoted to a detailed analysis of nonlocal error bounds for
nonconvex piecewise affine functions. We both improve some existing results on
error bounds for such functions and present completely new necessary and/or
sufficient conditions for a piecewise affine function to have an error bound on
various types of bounded and unbounded sets. In particular, we show that any
piecewise affine function has an error bound on an arbitrary bounded set and
provide several types of easily verifiable sufficient conditions for such
functions to have an error bound on unbounded sets. We also present general
necessary and sufficient conditions for a piecewise affine function to have an
error bound on a finite union of polyhedral sets (in particular, to have a
global error bound), whose derivation reveals a structure of sublevel sets and
recession functions of piecewise affine functions
On Verifiable Sufficient Conditions for Sparse Signal Recovery via Minimization
We propose novel necessary and sufficient conditions for a sensing matrix to
be "-good" - to allow for exact -recovery of sparse signals with
nonzero entries when no measurement noise is present. Then we express the error
bounds for imperfect -recovery (nonzero measurement noise, nearly
-sparse signal, near-optimal solution of the optimization problem yielding
the -recovery) in terms of the characteristics underlying these
conditions. Further, we demonstrate (and this is the principal result of the
paper) that these characteristics, although difficult to evaluate, lead to
verifiable sufficient conditions for exact sparse -recovery and to
efficiently computable upper bounds on those for which a given sensing
matrix is -good. We establish also instructive links between our approach
and the basic concepts of the Compressed Sensing theory, like Restricted
Isometry or Restricted Eigenvalue properties
- …