2,445 research outputs found
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
No penalty no tears: Least squares in high-dimensional linear models
Ordinary least squares (OLS) is the default method for fitting linear models,
but is not applicable for problems with dimensionality larger than the sample
size. For these problems, we advocate the use of a generalized version of OLS
motivated by ridge regression, and propose two novel three-step algorithms
involving least squares fitting and hard thresholding. The algorithms are
methodologically simple to understand intuitively, computationally easy to
implement efficiently, and theoretically appealing for choosing models
consistently. Numerical exercises comparing our methods with penalization-based
approaches in simulations and data analyses illustrate the great potential of
the proposed algorithms.Comment: Added results for non-sparse models; Added results for elliptical
distribution; Added simulations for adaptive lass
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