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In this paper, we consider a general sparse recovery and blind demodulation model. Different from the ones in the literature, in our general model, each dictionary atom undergoes a distinct modulation process; we refer to this as non-stationary modulation. We also assume that the modulation matrices live in a known subspace. Through the lifting technique, the sparse recovery and blind demodulation problem can be reformulated as a column-wise sparse matrix recovery problem, and we are able to recover both the sparse source signal and a cluster of modulation matrices via atomic norm and the induced ` 2,1 norm minimizations. Moreover, we show that the sampling complexity for exact recovery is proportional to the number of degrees of freedom up to log factors in the noiseless case. We also bound the recovery error in terms of the norm of the noise when the observation is noisy. Numerical simulations are conducted to illustrate our results.
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Robustness of Recovery in Locating Array-based Screening Experiments
Locating arrays (LAs) are experimental designs for screening interactions in engineered systems. LAs are often highly unbalanced, requiring advanced techniques to recover the terms that significantly influence system performance. While perfect recovery is achieved in the absence of noise, real systems are noisy. Therefore, in this paper, we study the robustness of recovery in the presence of noise. Using known models to generate synthetic data, we investigate recovery accuracy as a function of noise. Separation is introduced into LAs to allow more coverage for each t-way interaction; when separation is higher, recovery in noisy scenarios should improve. We find that locating arrays are able to recover the influential terms even with high levels of noise and that separation appears to improve recovery. Under the pessimistic assumption that noise depends on the range of responses, it is no surprise that terms with small coefficients become indistinguishable from noise.
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- Award ID(s):
- 1813729
- PAR ID:
- 10118966
- Date Published:
- Journal Name:
- Spring Simulation Multiconference
- ISSN:
- 2330-5622
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Locating arrays are designs used in combinatorial testing with the property that every set of d t-way interactions appears in a unique set of tests. Using a locating array to conduct fault testing ensures that faulty interactions can be located when there are d or fewer faults. Locating arrays are fairly new and few techniques have been explored for their construction. Most of the available work is limited to finding only one fault. Known general methods require a covering array of strength t+d and produce many more tests than are needed. We present Partitioned Search with Column Resampling (PSCR), a randomized computational search algorithmic framework to verify if an array is (d t)-locating by partitioning the search space to decrease the number of comparisons. If a candidate array is not locating, random resampling is performed until a locating array is constructed or an iteration limit is reached. Results are compared against known locating array constructions from covering arrays of higher strength and against published results of mixed level locating arrays for parameters of real-world systems. The use of PSCR to build larger locating arrays from a variety of ingredient arrays is explored.more » « less
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