5,348 research outputs found
Fast Graph Sampling Set Selection Using Gershgorin Disc Alignment
Graph sampling set selection, where a subset of nodes are chosen to collect
samples to reconstruct a smooth graph signal, is a fundamental problem in graph
signal processing (GSP). Previous works employ an unbiased least-squares (LS)
signal reconstruction scheme and select samples via expensive extreme
eigenvector computation. Instead, we assume a biased graph Laplacian
regularization (GLR) based scheme that solves a system of linear equations for
reconstruction. We then choose samples to minimize the condition number of the
coefficient matrix---specifically, maximize the smallest eigenvalue
. Circumventing explicit eigenvalue computation, we maximize
instead the lower bound of , designated by the smallest
left-end of all Gershgorin discs of the matrix. To achieve this efficiently, we
first convert the optimization to a dual problem, where we minimize the number
of samples needed to align all Gershgorin disc left-ends at a chosen
lower-bound target . Algebraically, the dual problem amounts to optimizing
two disc operations: i) shifting of disc centers due to sampling, and ii)
scaling of disc radii due to a similarity transformation of the matrix. We
further reinterpret the dual as an intuitive disc coverage problem bearing
strong resemblance to the famous NP-hard set cover (SC) problem. The
reinterpretation enables us to derive a fast approximation scheme from a known
SC error-bounded approximation algorithm. We find an appropriate target
efficiently via binary search. Extensive simulation experiments show that our
disc-based sampling algorithm runs substantially faster than existing sampling
schemes and outperforms other eigen-decomposition-free sampling schemes in
reconstruction error.Comment: Very fast deterministic graph sampling set selection algorithm
without explicit eigen-decompositio
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Efficient DSP and Circuit Architectures for Massive MIMO: State-of-the-Art and Future Directions
Massive MIMO is a compelling wireless access concept that relies on the use
of an excess number of base-station antennas, relative to the number of active
terminals. This technology is a main component of 5G New Radio (NR) and
addresses all important requirements of future wireless standards: a great
capacity increase, the support of many simultaneous users, and improvement in
energy efficiency. Massive MIMO requires the simultaneous processing of signals
from many antenna chains, and computational operations on large matrices. The
complexity of the digital processing has been viewed as a fundamental obstacle
to the feasibility of Massive MIMO in the past. Recent advances on
system-algorithm-hardware co-design have led to extremely energy-efficient
implementations. These exploit opportunities in deeply-scaled silicon
technologies and perform partly distributed processing to cope with the
bottlenecks encountered in the interconnection of many signals. For example,
prototype ASIC implementations have demonstrated zero-forcing precoding in real
time at a 55 mW power consumption (20 MHz bandwidth, 128 antennas, multiplexing
of 8 terminals). Coarse and even error-prone digital processing in the antenna
paths permits a reduction of consumption with a factor of 2 to 5. This article
summarizes the fundamental technical contributions to efficient digital signal
processing for Massive MIMO. The opportunities and constraints on operating on
low-complexity RF and analog hardware chains are clarified. It illustrates how
terminals can benefit from improved energy efficiency. The status of technology
and real-life prototypes discussed. Open challenges and directions for future
research are suggested.Comment: submitted to IEEE transactions on signal processin
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
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