1,073 research outputs found
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Lite it fly: An All-Deformable-Butterfly Network
Most deep neural networks (DNNs) consist fundamentally of convolutional
and/or fully connected layers, wherein the linear transform can be cast as the
product between a filter matrix and a data matrix obtained by arranging feature
tensors into columns. The lately proposed deformable butterfly (DeBut)
decomposes the filter matrix into generalized, butterflylike factors, thus
achieving network compression orthogonal to the traditional ways of pruning or
low-rank decomposition. This work reveals an intimate link between DeBut and a
systematic hierarchy of depthwise and pointwise convolutions, which explains
the empirically good performance of DeBut layers. By developing an automated
DeBut chain generator, we show for the first time the viability of homogenizing
a DNN into all DeBut layers, thus achieving an extreme sparsity and
compression. Various examples and hardware benchmarks verify the advantages of
All-DeBut networks. In particular, we show it is possible to compress a
PointNet to < 5% parameters with < 5% accuracy drop, a record not achievable by
other compression schemes.Comment: 7 pages, 3 figures, accepted as a brief paper in IEEE Transactions on
Neural Networks and Learning Systems (TNNLS
Sparse Approximate Multifrontal Factorization with Butterfly Compression for High Frequency Wave Equations
We present a fast and approximate multifrontal solver for large-scale sparse
linear systems arising from finite-difference, finite-volume or finite-element
discretization of high-frequency wave equations. The proposed solver leverages
the butterfly algorithm and its hierarchical matrix extension for compressing
and factorizing large frontal matrices via graph-distance guided entry
evaluation or randomized matrix-vector multiplication-based schemes. Complexity
analysis and numerical experiments demonstrate
computation and memory complexity when applied to an sparse system arising from 3D high-frequency Helmholtz and Maxwell problems
Image Restoration Using Joint Statistical Modeling in Space-Transform Domain
This paper presents a novel strategy for high-fidelity image restoration by
characterizing both local smoothness and nonlocal self-similarity of natural
images in a unified statistical manner. The main contributions are three-folds.
First, from the perspective of image statistics, a joint statistical modeling
(JSM) in an adaptive hybrid space-transform domain is established, which offers
a powerful mechanism of combining local smoothness and nonlocal self-similarity
simultaneously to ensure a more reliable and robust estimation. Second, a new
form of minimization functional for solving image inverse problem is formulated
using JSM under regularization-based framework. Finally, in order to make JSM
tractable and robust, a new Split-Bregman based algorithm is developed to
efficiently solve the above severely underdetermined inverse problem associated
with theoretical proof of convergence. Extensive experiments on image
inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise
removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions
on Circuits System and Video Technology (TCSVT). High resolution pdf version
and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM
Solving the Wide-band Inverse Scattering Problem via Equivariant Neural Networks
This paper introduces a novel deep neural network architecture for solving
the inverse scattering problem in frequency domain with wide-band data, by
directly approximating the inverse map, thus avoiding the expensive
optimization loop of classical methods. The architecture is motivated by the
filtered back-projection formula in the full aperture regime and with
homogeneous background, and it leverages the underlying equivariance of the
problem and compressibility of the integral operator. This drastically reduces
the number of training parameters, and therefore the computational and sample
complexity of the method. In particular, we obtain an architecture whose number
of parameters scale sub-linearly with respect to the dimension of the inputs,
while its inference complexity scales super-linearly but with very small
constants. We provide several numerical tests that show that the current
approach results in better reconstruction than optimization-based techniques
such as full-waveform inversion, but at a fraction of the cost while being
competitive with state-of-the-art machine learning methods.Comment: 21 pages, 9 figures, and 4 table
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