Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Generalised Differential Framework for Measuring Signal Sparsity   The notion of signal sparsity has been gaining increasing interest in
information theory and signal processing communities. As a consequence, a
plethora of sparsity metrics has been presented in the literature. The
appropriateness of these metrics is typically evaluated against a set of
objective criteria that has been proposed for assessing the credibility of any
sparsity metric. In this paper, we propose a Generalised Differential Sparsity
(GDS) framework for generating novel sparsity metrics whose functionality is
based on the concept that sparsity is encoded in the differences among the
signal coefficients. We rigorously prove that every metric generated using GDS
satisfies all the aforementioned criteria and we provide a computationally
efficient formula that makes GDS suitable for high-dimensional signals. The
great advantage of GDS is its flexibility to offer sparsity metrics that can be
well-tailored to certain requirements stemming from the nature of the data and
the problem to be solved. This is in contrast to current state-of-the-art
sparsity metrics like Gini Index (GI), which is actually proven to be only a
specific instance of GDS, demonstrating the generalisation power of our
framework. In verifying our claims, we have incorporated GDS in a stochastic
signal recovery algorithm and experimentally investigated its efficacy in
reconstructing randomly projected sparse signals. As a result, it is proven
that GDS, in comparison to GI, both loosens the bounds of the assumed sparsity
of the original signals and reduces the minimum number of projected dimensions,
required to guarantee an almost perfect reconstruction of heavily compressed
signals. The superiority of GDS over GI in conjunction with the fact that the
latter is considered as a standard in numerous scientific domains, prove the
great potential of GDS as a general purpose framework for measuring sparsity.

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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg