51,195 research outputs found
Focal-plane wavefront sensing with high-order adaptive optics systems
We investigate methods to calibrate the non-common path aberrations at an
adaptive optics system having a wavefront-correcting device working at an
extremely high resolution (larger than 150x150). We use focal-plane images
collected successively, the corresponding phase-diversity information and
numerically efficient algorithms to calculate the required wavefront updates.
The wavefront correction is applied iteratively until the algorithms converge.
Different approaches are studied. In addition of the standard Gerchberg-Saxton
algorithm, we test the extension of the Fast & Furious algorithm that uses
three images and creates an estimate of the pupil amplitudes. We also test
recently proposed phase-retrieval methods based on convex optimisation. The
results indicate that in the framework we consider, the calibration task is
easiest with algorithms similar to the Fast & Furious.Comment: 11 pages, 7 figures, published in SPIE proceeding
An Online Parallel and Distributed Algorithm for Recursive Estimation of Sparse Signals
In this paper, we consider a recursive estimation problem for linear
regression where the signal to be estimated admits a sparse representation and
measurement samples are only sequentially available. We propose a convergent
parallel estimation scheme that consists in solving a sequence of
-regularized least-square problems approximately. The proposed scheme
is novel in three aspects: i) all elements of the unknown vector variable are
updated in parallel at each time instance, and convergence speed is much faster
than state-of-the-art schemes which update the elements sequentially; ii) both
the update direction and stepsize of each element have simple closed-form
expressions, so the algorithm is suitable for online (real-time)
implementation; and iii) the stepsize is designed to accelerate the convergence
but it does not suffer from the common trouble of parameter tuning in
literature. Both centralized and distributed implementation schemes are
discussed. The attractive features of the proposed algorithm are also
numerically consolidated.Comment: Part of this work has been presented at The Asilomar Conference on
Signals, Systems, and Computers, Nov. 201
Outlier Detection Using Nonconvex Penalized Regression
This paper studies the outlier detection problem from the point of view of
penalized regressions. Our regression model adds one mean shift parameter for
each of the data points. We then apply a regularization favoring a sparse
vector of mean shift parameters. The usual penalty yields a convex
criterion, but we find that it fails to deliver a robust estimator. The
penalty corresponds to soft thresholding. We introduce a thresholding (denoted
by ) based iterative procedure for outlier detection (-IPOD). A
version based on hard thresholding correctly identifies outliers on some hard
test problems. We find that -IPOD is much faster than iteratively
reweighted least squares for large data because each iteration costs at most
(and sometimes much less) avoiding an least squares estimate.
We describe the connection between -IPOD and -estimators. Our
proposed method has one tuning parameter with which to both identify outliers
and estimate regression coefficients. A data-dependent choice can be made based
on BIC. The tuned -IPOD shows outstanding performance in identifying
outliers in various situations in comparison to other existing approaches. This
methodology extends to high-dimensional modeling with , if both the
coefficient vector and the outlier pattern are sparse
Network Flow Algorithms for Structured Sparsity
We consider a class of learning problems that involve a structured
sparsity-inducing norm defined as the sum of -norms over groups of
variables. Whereas a lot of effort has been put in developing fast optimization
methods when the groups are disjoint or embedded in a specific hierarchical
structure, we address here the case of general overlapping groups. To this end,
we show that the corresponding optimization problem is related to network flow
optimization. More precisely, the proximal problem associated with the norm we
consider is dual to a quadratic min-cost flow problem. We propose an efficient
procedure which computes its solution exactly in polynomial time. Our algorithm
scales up to millions of variables, and opens up a whole new range of
applications for structured sparse models. We present several experiments on
image and video data, demonstrating the applicability and scalability of our
approach for various problems.Comment: accepted for publication in Adv. Neural Information Processing
Systems, 201
- …