Denoising deterministic networks using iterative Fourier transforms

We detail a novel Fourier-based approach (IterativeFT) for identifying deterministic network structure in the presence of both edge pruning and Gaussian noise. This technique involves the iterative execution of forward and inverse 2D discrete Fourier transforms on a target network adjacency matrix. The denoising ability of the method is achieved via the application of a sparsification operation to both the real and frequency domain representations of the adjacency matrix with algorithm convergence achieved when the real domain sparsity pattern stabilizes. To demonstrate the effectiveness of the approach, we apply it to noisy versions of several deterministic models including Kautz, lattice, tree and bipartite networks. For contrast, we also evaluate preferential attachment networks to illustrate the behavior on stochastic graphs. We compare the performance of IterativeFT against simple real domain and frequency domain thresholding, reduced rank reconstruction and locally adaptive network sparsification. Relative to the comparison network denoising approaches, the proposed IterativeFT method provides the best overall performance for lattice and Kuatz networks with competitive performance on tree and bipartite networks. Importantly, the InterativeFT technique is effective at both filtering noisy edges and recovering true edges that are missing from the observed network.

Iterative execution of discrete and inverse discrete Fourier transforms with applications for signal denoising via sparsification

We describe a family of iterative algorithms that involve the repeated execution of discrete and inverse discrete Fourier transforms. One interesting member of this family is motivated by the discrete Fourier transform uncertainty principle and involves the application of a sparsification operation to both the time domain and frequency domain data with convergence obtained when time domain sparsity hits a stable pattern. This sparsification variant has practical utility for signal denoising, in particular the recovery of a periodic spike signal in the presence of Gaussian noise. General convergence properties and denoising performance are demonstrated using simulation studies. We are not aware of prior work on such iterative Fourier transformation algorithms and are posting this short paper in part to solicit feedback from others in the field who may be familiar with similar techniques.