8,163 research outputs found
Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion
A spectrally sparse signal of order is a mixture of damped or
undamped complex sinusoids. This paper investigates the problem of
reconstructing spectrally sparse signals from a random subset of regular
time domain samples, which can be reformulated as a low rank Hankel matrix
completion problem. We introduce an iterative hard thresholding (IHT) algorithm
and a fast iterative hard thresholding (FIHT) algorithm for efficient
reconstruction of spectrally sparse signals via low rank Hankel matrix
completion. Theoretical recovery guarantees have been established for FIHT,
showing that number of samples are sufficient for exact
recovery with high probability. Empirical performance comparisons establish
significant computational advantages for IHT and FIHT. In particular, numerical
simulations on D arrays demonstrate the capability of FIHT on handling large
and high-dimensional real data
Robust Dynamic Selection of Tested Modules in Software Testing for Maximizing Delivered Reliability
Software testing is aimed to improve the delivered reliability of the users.
Delivered reliability is the reliability of using the software after it is
delivered to the users. Usually the software consists of many modules. Thus,
the delivered reliability is dependent on the operational profile which
specifies how the users will use these modules as well as the defect number
remaining in each module. Therefore, a good testing policy should take the
operational profile into account and dynamically select tested modules
according to the current state of the software during the testing process. This
paper discusses how to dynamically select tested modules in order to maximize
delivered reliability by formulating the selection problem as a dynamic
programming problem. As the testing process is performed only once, risk must
be considered during the testing process, which is described by the tester's
utility function in this paper. Besides, since usually the tester has no
accurate estimate of the operational profile, by employing robust optimization
technique, we analysis the selection problem in the worst case, given the
uncertainty set of operational profile. By numerical examples, we show the
necessity of maximizing delivered reliability directly and using robust
optimization technique when the tester has no clear idea of the operational
profile. Moreover, it is shown that the risk averse behavior of the tester has
a major influence on the delivered reliability.Comment: 19 pages, 4 figure
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