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# Tidal river dynamics: Implications for deltas : TIDAL RIVER DYNAMICS

,

Reviews of Geophysics

Wiley

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### Most cited references144

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### Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE

(2002)
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### Mass Transport in Water Waves

(1953)
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• Abstract: found
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Is Open Access

### Sparsity and Incoherence in Compressive Sampling

(2006)
We consider the problem of reconstructing a sparse signal $$x^0\in\R^n$$ from a limited number of linear measurements. Given $$m$$ randomly selected samples of $$U x^0$$, where $$U$$ is an orthonormal matrix, we show that $$\ell_1$$ minimization recovers $$x^0$$ exactly when the number of measurements exceeds $m\geq \mathrm{Const}\cdot\mu^2(U)\cdot S\cdot\log n,$ where $$S$$ is the number of nonzero components in $$x^0$$, and $$\mu$$ is the largest entry in $$U$$ properly normalized: $$\mu(U) = \sqrt{n} \cdot \max_{k,j} |U_{k,j}|$$. The smaller $$\mu$$, the fewer samples needed. The result holds for most'' sparse signals $$x^0$$ supported on a fixed (but arbitrary) set $$T$$. Given $$T$$, if the sign of $$x^0$$ for each nonzero entry on $$T$$ and the observed values of $$Ux^0$$ are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples.
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### Author and article information

###### Journal
Reviews of Geophysics
Rev. Geophys.
Wiley
87551209
March 2016
March 31 2016
: 54
: 1
: 240-272
###### Article
10.1002/2015RG000507