High-dimensional sparse FFT based on sampling along multiple rank-1 lattices

The reconstruction of high-dimensional sparse signals is a challenging task in wide range applications. In order to deal with problems, efficient fast Fourier transform algorithms are essential tools. second and third authors have recently proposed dimension-incremental approach, which only scales almost linear the number required sampling values quadratic arithmetic complexity respect spatial dimension d. Using reconstructing rank-1 lattices as scheme, method showed reliable results numerical tests but suffers from relatively large numbers samples operations. Combining preferable properties small sample complexities, first author developed concept multiple lattices. this paper, both concepts — coupled, yields distinctly improved transform. Moreover, resulting algorithm analyzed detail success probability, samples, complexity. comparison single lattices, utilization reduction complexities by an factor sparsity. Various confirm theoretical results, high performance, reliability method.