19,991 research outputs found
2-D iteratively reweighted least squares lattice algorithm and its application to defect detection in textured images
In this paper, a 2-D iteratively reweighted least squares lattice algorithm, which is robust to the outliers, is introduced and is applied to defect detection problem in textured images. First, the philosophy of using different optimization functions that results in weighted least squares solution in the theory of 1-D robust regression is extended to 2-D. Then a new algorithm is derived which combines 2-D robust regression concepts with the 2-D recursive least squares lattice algorithm. With this approach, whatever the probability distribution of the prediction error may be, small weights are assigned to the outliers so that the least squares algorithm will be less sensitive to the outliers. Implementation of the proposed iteratively reweighted least squares lattice algorithm to the problem of defect detection in textured images is then considered. The performance evaluation, in terms of defect detection rate, demonstrates the importance of the proposed algorithm in reducing the effect of the outliers that generally correspond to false alarms in classification of textures as defective or nondefective
Distributed estimation from relative measurements of heterogeneous and uncertain quality
This paper studies the problem of estimation from relative measurements in a
graph, in which a vector indexed over the nodes has to be reconstructed from
pairwise measurements of differences between its components associated to nodes
connected by an edge. In order to model heterogeneity and uncertainty of the
measurements, we assume them to be affected by additive noise distributed
according to a Gaussian mixture. In this original setup, we formulate the
problem of computing the Maximum-Likelihood (ML) estimates and we design two
novel algorithms, based on Least Squares regression and
Expectation-Maximization (EM). The first algorithm (LS- EM) is centralized and
performs the estimation from relative measurements, the soft classification of
the measurements, and the estimation of the noise parameters. The second
algorithm (Distributed LS-EM) is distributed and performs estimation and soft
classification of the measurements, but requires the knowledge of the noise
parameters. We provide rigorous proofs of convergence of both algorithms and we
present numerical experiments to evaluate and compare their performance with
classical solutions. The experiments show the robustness of the proposed
methods against different kinds of noise and, for the Distributed LS-EM,
against errors in the knowledge of noise parameters.Comment: Submitted to IEEE transaction
A new ADMM algorithm for the Euclidean median and its application to robust patch regression
The Euclidean Median (EM) of a set of points in an Euclidean space
is the point x minimizing the (weighted) sum of the Euclidean distances of x to
the points in . While there exits no closed-form expression for the EM,
it can nevertheless be computed using iterative methods such as the Wieszfeld
algorithm. The EM has classically been used as a robust estimator of centrality
for multivariate data. It was recently demonstrated that the EM can be used to
perform robust patch-based denoising of images by generalizing the popular
Non-Local Means algorithm. In this paper, we propose a novel algorithm for
computing the EM (and its box-constrained counterpart) using variable splitting
and the method of augmented Lagrangian. The attractive feature of this approach
is that the subproblems involved in the ADMM-based optimization of the
augmented Lagrangian can be resolved using simple closed-form projections. The
proposed ADMM solver is used for robust patch-based image denoising and is
shown to exhibit faster convergence compared to an existing solver.Comment: 5 pages, 3 figures, 1 table. To appear in Proc. IEEE International
Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201
- …