6,222 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
Fast algorithms and efficient GPU implementations for the Radon transform and the back-projection operator represented as convolution operators
The Radon transform and its adjoint, the back-projection operator, can both
be expressed as convolutions in log-polar coordinates. Hence, fast algorithms
for the application of the operators can be constructed by using FFT, if data
is resampled at log-polar coordinates. Radon data is typically measured on an
equally spaced grid in polar coordinates, and reconstructions are represented
(as images) in Cartesian coordinates. Therefore, in addition to FFT, several
steps of interpolation have to be conducted in order to apply the Radon
transform and the back-projection operator by means of convolutions.
Both the interpolation and the FFT operations can be efficiently implemented
on Graphical Processor Units (GPUs). For the interpolation, it is possible to
make use of the fact that linear interpolation is hard-wired on GPUs, meaning
that it has the same computational cost as direct memory access. Cubic order
interpolation schemes can be constructed by combining linear interpolation
steps which provides important computation speedup.
We provide details about how the Radon transform and the back-projection can
be implemented efficiently as convolution operators on GPUs. For large data
sizes, speedups of about 10 times are obtained in relation to the computational
times of other software packages based on GPU implementations of the Radon
transform and the back-projection operator. Moreover, speedups of more than a
1000 times are obtained against the CPU-implementations provided in the MATLAB
image processing toolbox
Biorthogonal partners and applications
Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications
The Discrete radon transform: A more efficient approach to image reconstruction
The Radon transform and its inversion are the mathematical keys that enable tomography. Radon transforms are defined for continuous objects with continuous projections at all angles in [0,Ï). In practice, however, we pre-filter discrete projections take
An Efficient Algorithm for Video Super-Resolution Based On a Sequential Model
In this work, we propose a novel procedure for video super-resolution, that
is the recovery of a sequence of high-resolution images from its low-resolution
counterpart. Our approach is based on a "sequential" model (i.e., each
high-resolution frame is supposed to be a displaced version of the preceding
one) and considers the use of sparsity-enforcing priors. Both the recovery of
the high-resolution images and the motion fields relating them is tackled. This
leads to a large-dimensional, non-convex and non-smooth problem. We propose an
algorithmic framework to address the latter. Our approach relies on fast
gradient evaluation methods and modern optimization techniques for
non-differentiable/non-convex problems. Unlike some other previous works, we
show that there exists a provably-convergent method with a complexity linear in
the problem dimensions. We assess the proposed optimization method on {several
video benchmarks and emphasize its good performance with respect to the state
of the art.}Comment: 37 pages, SIAM Journal on Imaging Sciences, 201
Hypernetwork functional image representation
Motivated by the human way of memorizing images we introduce their functional
representation, where an image is represented by a neural network. For this
purpose, we construct a hypernetwork which takes an image and returns weights
to the target network, which maps point from the plane (representing positions
of the pixel) into its corresponding color in the image. Since the obtained
representation is continuous, one can easily inspect the image at various
resolutions and perform on it arbitrary continuous operations. Moreover, by
inspecting interpolations we show that such representation has some properties
characteristic to generative models. To evaluate the proposed mechanism
experimentally, we apply it to image super-resolution problem. Despite using a
single model for various scaling factors, we obtained results comparable to
existing super-resolution methods
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