564 research outputs found
A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding
2013 14th IEEE International Conference on Computer Vision, ICCV 2013, Sydney, NSW, 1-8 December 2013In many sparse coding based image restoration and image classification problems, using non-convex ℓp-norm minimization (0 ≤p <1) can often obtain better results than the convex ℓ1-norm minimization. A number of algorithms, e.g., iteratively reweighted least squares (IRLS), iteratively thresholding method (ITM-ℓp), and look-up table (LUT), have been proposed for non-convex ℓp-norm sparse coding, while some analytic solutions have been suggested for some specific values of p. In this paper, by extending the popular soft-thresholding operator, we propose a generalized iterated shrinkage algorithm (GISA) for ℓp-norm non-convex sparse coding. Unlike the analytic solutions, the proposed GISA algorithm is easy to implement, and can be adopted for solving non-convex sparse coding problems with arbitrary p values. Compared with LUT, GISA is more general and does not need to compute and store the look-up tables. Compared with IRLS and ITM-ℓp, GISA is theoretically more solid and can achieve more accurate solutions. Experiments on image restoration and sparse coding based face recognition are conducted to validate the performance of GISA.Department of ComputingRefereed conference pape
Image interpolation using Shearlet based iterative refinement
This paper proposes an image interpolation algorithm exploiting sparse
representation for natural images. It involves three main steps: (a) obtaining
an initial estimate of the high resolution image using linear methods like FIR
filtering, (b) promoting sparsity in a selected dictionary through iterative
thresholding, and (c) extracting high frequency information from the
approximation to refine the initial estimate. For the sparse modeling, a
shearlet dictionary is chosen to yield a multiscale directional representation.
The proposed algorithm is compared to several state-of-the-art methods to
assess its objective as well as subjective performance. Compared to the cubic
spline interpolation method, an average PSNR gain of around 0.8 dB is observed
over a dataset of 200 images
Weighted Schatten -Norm Minimization for Image Denoising and Background Subtraction
Low rank matrix approximation (LRMA), which aims to recover the underlying
low rank matrix from its degraded observation, has a wide range of applications
in computer vision. The latest LRMA methods resort to using the nuclear norm
minimization (NNM) as a convex relaxation of the nonconvex rank minimization.
However, NNM tends to over-shrink the rank components and treats the different
rank components equally, limiting its flexibility in practical applications. We
propose a more flexible model, namely the Weighted Schatten -Norm
Minimization (WSNM), to generalize the NNM to the Schatten -norm
minimization with weights assigned to different singular values. The proposed
WSNM not only gives better approximation to the original low-rank assumption,
but also considers the importance of different rank components. We analyze the
solution of WSNM and prove that, under certain weights permutation, WSNM can be
equivalently transformed into independent non-convex -norm subproblems,
whose global optimum can be efficiently solved by generalized iterated
shrinkage algorithm. We apply WSNM to typical low-level vision problems, e.g.,
image denoising and background subtraction. Extensive experimental results
show, both qualitatively and quantitatively, that the proposed WSNM can more
effectively remove noise, and model complex and dynamic scenes compared with
state-of-the-art methods.Comment: 13 pages, 11 figure
Ship Wake Detection in SAR Images via Sparse Regularization
In order to analyse synthetic aperture radar (SAR) images of the sea surface,
ship wake detection is essential for extracting information on the wake
generating vessels. One possibility is to assume a linear model for wakes, in
which case detection approaches are based on transforms such as Radon and
Hough. These express the bright (dark) lines as peak (trough) points in the
transform domain. In this paper, ship wake detection is posed as an inverse
problem, which the associated cost function including a sparsity enforcing
penalty, i.e. the generalized minimax concave (GMC) function. Despite being a
non-convex regularizer, the GMC penalty enforces the overall cost function to
be convex. The proposed solution is based on a Bayesian formulation, whereby
the point estimates are recovered using maximum a posteriori (MAP) estimation.
To quantify the performance of the proposed method, various types of SAR images
are used, corresponding to TerraSAR-X, COSMO-SkyMed, Sentinel-1, and ALOS2. The
performance of various priors in solving the proposed inverse problem is first
studied by investigating the GMC along with the L1, Lp, nuclear and total
variation (TV) norms. We show that the GMC achieves the best results and we
subsequently study the merits of the corresponding method in comparison to two
state-of-the-art approaches for ship wake detection. The results show that our
proposed technique offers the best performance by achieving 80% success rate.Comment: 18 page
Deep Network Classification by Scattering and Homotopy Dictionary Learning
We introduce a sparse scattering deep convolutional neural network, which
provides a simple model to analyze properties of deep representation learning
for classification. Learning a single dictionary matrix with a classifier
yields a higher classification accuracy than AlexNet over the ImageNet 2012
dataset. The network first applies a scattering transform that linearizes
variabilities due to geometric transformations such as translations and small
deformations. A sparse dictionary coding reduces intra-class
variability while preserving class separation through projections over unions
of linear spaces. It is implemented in a deep convolutional network with a
homotopy algorithm having an exponential convergence. A convergence proof is
given in a general framework that includes ALISTA. Classification results are
analyzed on ImageNet
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