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(Color online) (a) The StRIP is plotted for the Golomb, best and worst of 200 random arrays. These arrays have length 128 with 14 elements. The Golomb array possesses a smaller StRIP than either of the two random arrays. However, the best random array has StRIP values very close to those of the Golomb array. (b) The null space property is plotted for the Golomb, worst and best random arrays over the range 2 ≤ k ≤ 14, but the null space property is determined with 2k sparse components. The rank of is only 14; there are 14 directions that do not contribute to the data. (c) The StRIP is plotted for the Wichmann array, the best and worst of 200 random arrays. These arrays have lengths 124 with 19 elements. The Wichmann array has a StRIP that is never smaller than the best random array and is sometimes greater than the worst random array.
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(Color online) Bearing time (BT) plots for three arrays computed from data from the Five Octave Research Array (FORA). Each BT plot shows the incoherent average from 100 to 250 Hz. (a) The conventional array shows poor resolution, especially in the regions near endfire. (b) The Golomb array displays higher resolution than the conventional in all regions. Note the resolution of the source at approximately 10°. (c) The BT plot of the Wichmann subsampled array shows remarkably worse performance than the Golomb subsampled array. The quiet source at approximately 30° is nearly absent.
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The numerical application of the statistical reduced isometry property (StRIP) and statistical null space property (SNSP) is presented and demonstrated for the design of underwater acoustic line arrays. This recent approach predicts the theoretical utility of specific subsampled arrays for compressive sensing. Three subsamplings are presented: Random, Golomb, and Wichmann. The Golomb array has no repeated spacings. The Wichmann array includes every possible interval of spacings. The SNSP is shown insensitive to the cases presented. The StRIP of the Golomb array predicts superior invertibility and is shown to perform well using at-sea data.
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