We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of the minimax risk. However, when the set is unspecified, designing an estimator that is blind to the hidden structure of the signal remains a challenging problem. We propose a new family of estimators to recover signals observed in Gaussian noise. Instead of specifying the set where the signal lives, we assume the existence of a well-performing linear estimator. Proposed estimators enjoy exact oracle inequalities and can be efficiently computed through convex optimization.

LargeNumberofNodes In this section, we test DAGMA, GOLEM, and NOTEARS for graphs with number of variables d {200,300,500,800,1000}.

However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility)

Figure 1: R-Blur adds Gaussian noise to image (a) with the fixation point (red dot) to obtain (b).

Many practical settings call for the reconstruction of temporal signals from corrupted or missing data. Classic examples include decoding, tracking, signal enhancement and denoising.

Though the background is pure white, the target object is also white.