Cuyt A, Hou Y, Knaepkens F & Lee W (2020) Sparse multidimensional exponential analysis with an application to radar imaging. SIAM Journal on Scientific Computing, 42 (3), p. B675–B695. https://doi.org/10.1137/19M1278004
We present a d-dimensional exponential analysis algorithm that offers a range of advantages compared to other methods. The technique does not suffer the curse of dimensionality and only needs O((d + 1)n) samples for the analysis of an n-sparse expression. It does not require a prior estimate of the sparsity n of the d-variate exponential sum. The method can work with sub-Nyquist sampled data and offers a validation step, which is very useful in low SNR conditions. A favourable computation cost results from the fact that d independent smaller systems are solved instead of one large system incorporating all measurements simultaneously. So the method also lends itself easily to a parallel execution. Our motivation to develop the technique comes from 2D and 3D radar imaging and is therefore illustrated on such examples.
exponentional analysis; parametric method; multidimensional; sparse model; sparse data; inverse problems
SIAM Journal on Scientific Computing: Volume 42, Issue 3