Approximative covariance interpolation with a quadratic penalty

Image compression by means of the multidimensional circulant covariance extension problem – Revisited

“…The covariance extension problem has been formerly studied to design high resolution spectral estimators for stationary stochastic processes, [1], [15], [22], [30] including the approximate moments matching case [4], [13]. Within this framework, an important aspect is that it is possible to take as objective function a pseudo-distance (or divergence) between the spectral density to be estimated and a given spectral density, called prior.…”

Learning AR factor models

“…Trace norm regularization is also used in the so called latent-variable auto-regressive (AR) graphical models, [8], [11], [24], [26] where we learn the spectral density of the model such that its inverse admits a "sparse plus low-rank decomposition". It is worth noting that data enters in these estimators through an approximate moments matching, in a similar spirit of [15]. This is a wise way to use moments.…”

Multidimensional Rational Covariance Extension with Approximate Covariance Matching

“…As will be explained in Section 2, D(P dm, dµ) is always nonnegative and has the property D(P dm, P dm) = 0. In this paper we shall consider a more general problem in the spirit of [22]. To this end, for any Hermitian, positive definite matrix M , we define the weighted vector norm subject to r k = T d e i(k,θ) dµ(θ), k ∈ Λ, which is the same as the problem above with W = λI.…”

“…For example, an absolute error estimate for the covariances is more naturally incorporated in the formulation with hard constraints. A possible choice of the weight matrix W in either formulation would be the covariance matrix of the estimated moments, as suggested in [22]. This corresponds to the Mahalanobis distance and could be a natural way to incorporate uncertainty of the covariance estimates in the spectral estimation procedure.…”

“…Previous work in this direction can be found in [10,22,35,57,58], where [10,35,58] consider the problem of selecting an appropriate covariances sequence to match in a given confidence region. The two approximation problems considered here are similar to the ones considered in [57] and [22]. (For more details, also see [3, Ch.…”