78 research outputs found
The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing
This paper deals with the computational complexity of conditions which
guarantee that the NP-hard problem of finding the sparsest solution to an
underdetermined linear system can be solved by efficient algorithms. In the
literature, several such conditions have been introduced. The most well-known
ones are the mutual coherence, the restricted isometry property (RIP), and the
nullspace property (NSP). While evaluating the mutual coherence of a given
matrix is easy, it has been suspected for some time that evaluating RIP and NSP
is computationally intractable in general. We confirm these conjectures by
showing that for a given matrix A and positive integer k, computing the best
constants for which the RIP or NSP hold is, in general, NP-hard. These results
are based on the fact that determining the spark of a matrix is NP-hard, which
is also established in this paper. Furthermore, we also give several complexity
statements about problems related to the above concepts.Comment: 13 pages; accepted for publication in IEEE Trans. Inf. Theor
DOLPHIn - Dictionary Learning for Phase Retrieval
We propose a new algorithm to learn a dictionary for reconstructing and
sparsely encoding signals from measurements without phase. Specifically, we
consider the task of estimating a two-dimensional image from squared-magnitude
measurements of a complex-valued linear transformation of the original image.
Several recent phase retrieval algorithms exploit underlying sparsity of the
unknown signal in order to improve recovery performance. In this work, we
consider such a sparse signal prior in the context of phase retrieval, when the
sparsifying dictionary is not known in advance. Our algorithm jointly
reconstructs the unknown signal - possibly corrupted by noise - and learns a
dictionary such that each patch of the estimated image can be sparsely
represented. Numerical experiments demonstrate that our approach can obtain
significantly better reconstructions for phase retrieval problems with noise
than methods that cannot exploit such "hidden" sparsity. Moreover, on the
theoretical side, we provide a convergence result for our method
Joint Antenna Selection and Phase-Only Beamforming Using Mixed-Integer Nonlinear Programming
In this paper, we consider the problem of joint antenna selection and analog
beamformer design in downlink single-group multicast networks. Our objective is
to reduce the hardware costs by minimizing the number of required phase
shifters at the transmitter while fulfilling given distortion limits at the
receivers. We formulate the problem as an L0 minimization problem and devise a
novel branch-and-cut based algorithm to solve the resulting mixed-integer
nonlinear program to optimality. We also propose a suboptimal heuristic
algorithm to solve the above problem approximately with a low computational
complexity. Computational results illustrate that the solutions produced by the
proposed heuristic algorithm are optimal in most cases. The results also
indicate that the performance of the optimal methods can be significantly
improved by initializing with the result of the suboptimal method.Comment: to be presented at WSA 201
Extended Successive Convex Approximation for Phase Retrieval with Dictionary Learning
Phase retrieval aims at reconstructing unknown signals from magnitude
measurements of linear mixtures. In this paper, we consider the phase retrieval
with dictionary learning problem, which includes an additional prior
information that the measured signal admits a sparse representation over an
unknown dictionary. The task is to jointly estimate the dictionary and the
sparse representation from magnitude-only measurements. To this end, we study
two complementary formulations and develop efficient parallel algorithms by
extending the successive convex approximation framework using a smooth
majorization. The first algorithm is termed compact-SCAphase and is preferable
in the case of less diverse mixture models. It employs a compact formulation
that avoids the use of auxiliary variables. The proposed algorithm is highly
scalable and has reduced parameter tuning cost. The second algorithm, referred
to as SCAphase, uses auxiliary variables and is favorable in the case of highly
diverse mixture models. It also renders simple incorporation of additional side
constraints. The performance of both methods is evaluated when applied to blind
sparse channel estimation from subband magnitude measurements in a
multi-antenna random access network. Simulation results demonstrate the
efficiency of the proposed techniques compared to state-of-the-art methods.Comment: This work has been submitted to the IEEE Transactions on Signal
Processing for possible publication. Copyright may be transferred without
notice, after which this version may no longer be accessibl
Extending the rapeseed gene pool with resynthesized Brassica napus II: Heterosis
Hybrid breeding relies on the combination of parents from two differing heterotic groups. However, the genetic diversity in adapted oilseed rape breeding material is rather limited. Therefore, the use of resynthesized Brassica napus as a distant gene pool was investigated. Hybrids were derived from crosses between 44 resynthesized lines with a diverse genetic background and two male sterile winter oilseed rape tester lines. The hybrids were evaluated together with their parents and check cultivars in 2 years and five locations in Germany. Yield, plant height, seed oil, and protein content were monitored, and genetic distances were estimated with molecular markers (127 polymorphic RFLP fragments). Resynthesized lines varied in yield between 40.9 dt/ha and 21.5 dt/ha, or between 85.1 and 44.6% of check cultivar yields. Relative to check cultivars, hybrids varied from 91.6 to 116.6% in yield and from 94.5 to 103.3% in seed oil content. Mid-parent heterosis varied from −3.5 to 47.2% for yield. The genetic distance of parental lines was not significantly correlated with heterosis or hybrid yield. Although resynthesized lines do not meet the elite rapeseed standards, they are a valuable source for hybrid breeding due to their large distance from present breeding material and their high heterosis when combined with European winter oilseed rape
Simvastatin add-on to escitalopram in patients with comorbid obesity and major depression (SIMCODE): study protocol of a multicentre, randomised, double-blind, placebo-controlled trial
Introduction: Major depressive disorder (MDD) and obesity are both common disorders associated with significant burden of disease worldwide. Importantly, MDD and obesity often co-occur, with each disorder increasing the risk for developing the other by about 50%-60%. Statins are among the most prescribed medications with well-established safety and efficacy. Statins are recommended in primary prevention of cardiovascular disease, which has been linked to both MDD and obesity. Moreover, statins are promising candidates to treat MDD because a meta-analysis of pilot randomised controlled trials has found antidepressive effects of statins as adjunct therapy to antidepressants. However, no study so far has tested the antidepressive potential of statins in patients with MDD and comorbid obesity. Importantly, this is a difficult-to-treat population that often exhibits a chronic course of MDD and is more likely to be treatment resistant. Thus, in this confirmatory randomised controlled trial, we will determine whether add-on simvastatin to standard antidepressant medication with escitalopram is more efficacious than add-on placebo over 12 weeks in 160 patients with MDD and comorbid obesity.
Methods and analysis: This is a protocol for a randomised, placebo-controlled, double-blind multicentre trial with parallel-group design (phase II). One hundred and sixty patients with MDD and comorbid obesity will be randomised 1:1 to simvastatin or placebo as add-on to standard antidepressant medication with escitalopram. The primary outcome is change in the Montgomery-angstrom sberg Depression Rating Scale (MADRS) score from baseline to week 12. Secondary outcomes include MADRS response (defined as 50% MADRS score reduction from baseline), MADRS remission (defined as MADRS score <10), mean change in patients' self-reported Beck Depression Inventory (BDI-II) and mean change in high-density lipoprotein, low-density lipoprotein and total cholesterol from baseline to week 12.
Ethics and dissemination: This protocol has been approved by the ethics committee of the federal state of Berlin (Ethik-Kommission des Landes Berlin, reference: 19/0226-EK 11) and by the relevant federal authority (Bundesinstitut fur Arzneimittel und Medizinprodukte (BfArM), reference: 4043387). Study findings will be published in peer-reviewed journals and will be presented at (inter)national conferences
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