4,028 research outputs found
Phase Retrieval From Binary Measurements
We consider the problem of signal reconstruction from quadratic measurements
that are encoded as +1 or -1 depending on whether they exceed a predetermined
positive threshold or not. Binary measurements are fast to acquire and
inexpensive in terms of hardware. We formulate the problem of signal
reconstruction using a consistency criterion, wherein one seeks to find a
signal that is in agreement with the measurements. To enforce consistency, we
construct a convex cost using a one-sided quadratic penalty and minimize it
using an iterative accelerated projected gradient-descent (APGD) technique. The
PGD scheme reduces the cost function in each iteration, whereas incorporating
momentum into PGD, notwithstanding the lack of such a descent property,
exhibits faster convergence than PGD empirically. We refer to the resulting
algorithm as binary phase retrieval (BPR). Considering additive white noise
contamination prior to quantization, we also derive the Cramer-Rao Bound (CRB)
for the binary encoding model. Experimental results demonstrate that the BPR
algorithm yields a signal-to- reconstruction error ratio (SRER) of
approximately 25 dB in the absence of noise. In the presence of noise prior to
quantization, the SRER is within 2 to 3 dB of the CRB
Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming
Given a linear system in a real or complex domain, linear regression aims to
recover the model parameters from a set of observations. Recent studies in
compressive sensing have successfully shown that under certain conditions, a
linear program, namely, l1-minimization, guarantees recovery of sparse
parameter signals even when the system is underdetermined. In this paper, we
consider a more challenging problem: when the phase of the output measurements
from a linear system is omitted. Using a lifting technique, we show that even
though the phase information is missing, the sparse signal can be recovered
exactly by solving a simple semidefinite program when the sampling rate is
sufficiently high, albeit the exact solutions to both sparse signal recovery
and phase retrieval are combinatorial. The results extend the type of
applications that compressive sensing can be applied to those where only output
magnitudes can be observed. We demonstrate the accuracy of the algorithms
through theoretical analysis, extensive simulations and a practical experiment.Comment: Parts of the derivations have submitted to the 16th IFAC Symposium on
System Identification, SYSID 2012, and parts to the 51st IEEE Conference on
Decision and Control, CDC 201
Sparse Signal Processing Concepts for Efficient 5G System Design
As it becomes increasingly apparent that 4G will not be able to meet the
emerging demands of future mobile communication systems, the question what
could make up a 5G system, what are the crucial challenges and what are the key
drivers is part of intensive, ongoing discussions. Partly due to the advent of
compressive sensing, methods that can optimally exploit sparsity in signals
have received tremendous attention in recent years. In this paper we will
describe a variety of scenarios in which signal sparsity arises naturally in 5G
wireless systems. Signal sparsity and the associated rich collection of tools
and algorithms will thus be a viable source for innovation in 5G wireless
system design. We will discribe applications of this sparse signal processing
paradigm in MIMO random access, cloud radio access networks, compressive
channel-source network coding, and embedded security. We will also emphasize
important open problem that may arise in 5G system design, for which sparsity
will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces
Roadmap on optical security
Postprint (author's final draft
Measure What Should be Measured: Progress and Challenges in Compressive Sensing
Is compressive sensing overrated? Or can it live up to our expectations? What
will come after compressive sensing and sparsity? And what has Galileo Galilei
got to do with it? Compressive sensing has taken the signal processing
community by storm. A large corpus of research devoted to the theory and
numerics of compressive sensing has been published in the last few years.
Moreover, compressive sensing has inspired and initiated intriguing new
research directions, such as matrix completion. Potential new applications
emerge at a dazzling rate. Yet some important theoretical questions remain
open, and seemingly obvious applications keep escaping the grip of compressive
sensing. In this paper I discuss some of the recent progress in compressive
sensing and point out key challenges and opportunities as the area of
compressive sensing and sparse representations keeps evolving. I also attempt
to assess the long-term impact of compressive sensing
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