2 research outputs found
Recovery analysis for weighted mixed minimization with
We study the recovery conditions of weighted mixed minimization for block sparse signal reconstruction from compressed
measurements when partial block support information is available. We show that
the block -restricted isometry property (RIP) can ensure the robust
recovery. Moreover, we present the sufficient and necessary condition for the
recovery by using weighted block -null space property. The relationship
between the block -RIP and the weighted block -null space property has
been established. Finally, we illustrate our results with a series of numerical
experiments
Coherence-Based Performance Guarantee of Regularized -Norm Minimization and Beyond
In this paper, we consider recovering the signal
from its few noisy measurements , where
with is the measurement matrix, and
is the measurement noise/error. We first establish a
coherence-based performance guarantee for a regularized -norm
minimization model to recover such signals in the presence of the
-norm bounded noise, i.e., , and then
extend these theoretical results to guarantee the robust recovery of the
signals corrupted with the Dantzig Selector (DS) type noise, i.e.,
, and the structured block-sparse signal
recovery in the presence of the bounded noise. To the best of our knowledge, we
first extend nontrivially the sharp uniform recovery condition derived by Cai,
Wang and Xu (2010) for the constrained -norm minimization model,
which takes the form of \begin{align*} \mu<\frac{1}{2k-1}, \end{align*} where
is defined as the (mutual) coherence of , to two unconstrained
regularized -norm minimization models to guarantee the robust
recovery of any signals (not necessary to be -sparse) under the
-norm bounded noise and the DS type noise settings, respectively.
Besides, a uniform recovery condition and its two resulting error estimates are
also established for the first time to our knowledge, for the robust
block-sparse signal recovery using a regularized mixed -norm
minimization model, and these results well complement the existing theoretical
investigation on this model which focuses on the non-uniform recovery
conditions and/or the robust signal recovery in presence of the random noise.Comment: 19 page