Title | ||
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A derandomization approach to recovering bandlimited signals across a wide range of random sampling rates. |
Abstract | ||
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Reconstructing bandlimited functions from random sampling is an important problem in signal processing. Strohmer and Vershynin obtained good results for this problem by using a randomized version of the Kaczmarz algorithm (RK) and assigning to every equation a probability weight proportional to the average distance of the sample from its two nearest neighbors. However, their results are valid only for moderate to high sampling rates; in practice, it may not always be possible to obtain many samples. Experiments show that the number of projections required by RK and other Kaczmarz variants rises seemingly exponentially when the equations/variables ratio (EVR) falls below 5. CGMN, which is a CG acceleration of Kaczmarz, provides very good results for low values of EVR and it is much better than CGNR and CGNE. A derandomization method, based on an extension of the bit-reversal permutation, is combined with the weights and shown to improve the performance of CGMN and the regular (cyclic) Kaczmarz, which even outperforms RK. A byproduct of our results is the finding that signals composed mainly of high-frequency components are easier to recover. |
Year | DOI | Venue |
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2018 | https://doi.org/10.1007/s11075-017-0356-3 | Numerical Algorithms |
Keywords | Field | DocType |
Bandlimited functions,Bit-reversal,CGMN,Derandomization,Extended bit-reversal,Low sampling rates,Randomized Kaczmarz,RK,Signal processing | Signal processing,Mathematical optimization,Bandlimiting,Permutation,Algorithm,Acceleration,Sampling (statistics),Mathematics,Exponential growth | Journal |
Volume | Issue | ISSN |
77 | 4 | 1017-1398 |
Citations | PageRank | References |
0 | 0.34 | 7 |
Authors | ||
1 |
Name | Order | Citations | PageRank |
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Dan Gordon | 1 | 210 | 21.44 |