English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We address the problem of estimating a random vector from two sets of measurements and , such that the estimator is linear in . We show that the partially linear minimum mean-square error (PLMMSE) estimator does not require knowing the joint distribution of and in full, but rather only its second-order moments. This renders it of potential interest in various applications. We further show that the PLMMSE method is minimax-optimal among all estimators that solely depend on the second-order statistics of and . We demonstrate our approach in the context of recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version. We show that in this setting PLMMSE estimation has a clear computational advantage, while its performance is comparable to state-of-the-art algorithms. We apply our approach both in static and in dynamic estimation applications. In the former category, we treat the problem of image enhancement from blurred/noisy image pairs. We show that PLMMSE estimation performs only slightly worse than state-of-the art algorithms, while running an order of magnitude faster. In the dynamic setting, we provide a recursive implementation of the estimator and demonstrate its utility in tracking maneuvering targets from position and acceleration measurements.

Partially Linear Estimation With Application to Sparse Signal Recovery From Measurement Pairs