Robust Reconstruction of Complex Networks from Sparse Data

Robust Reconstruction of Complex Networks from Sparse Data

Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural information hidden in limited amounts of data accompanied by noise and in the presence of inaccessible nodes. Here, we develop a general framework for robust ...

Sparse and Robust Signal Reconstruction

Many problems in signal processing and statistical inference are based on finding a sparse solution to an undetermined linear system. The reference approach to this problem of finding sparse signal representations, on overcomplete dictionaries, leads to convex unconstrained optimization problems, with a quadratic term l2, for the adjustment to the observed signal, and a coefficient vector l1-no...

Image Reconstruction from Incomplete Data

Image Reconstruction from Incomplete Data

Image reconstruction from photon sparse data

We report an algorithm for reconstructing images when the average number of photons recorded per pixel is of order unity, i.e. photon-sparse data. The image optimisation algorithm minimises a cost function incorporating both a Poissonian log-likelihood term based on the deviation of the reconstructed image from the measured data and a regularization-term based upon the sum of the moduli of the ...