Abstract
The goal of noisy high-dimensional phase retrieval is to estimate an s-sparse parameter β∗ ∈ ℝd from n realizations of the model Y = (XTβ∗)2 + ϵ. Based on this model, we propose a significant semi-parametric generalization called mis-specified phase retrieval (MPR), in which Y = f(XTβ∗,ϵ) with unknown f and Cov(Y, (XTβ∗)2) > 0. For example, MPR encompasses Y = h(|XTβ∗ |) + ϵ with increasing h as a special case. Despite the generality of the MPR model, it eludes the reach of most existing semi-parametric estimators. In this paper, we propose an estimation procedure, which consists of solving a cascade of two convex programs and provably recovers the direction of β∗. Our theory is backed up by thorough numerical results.
Original language | English (US) |
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Pages (from-to) | 4096-4104 |
Number of pages | 9 |
Journal | Advances in Neural Information Processing Systems |
State | Published - 2016 |
Event | 30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain Duration: Dec 5 2016 → Dec 10 2016 |
All Science Journal Classification (ASJC) codes
- Computer Networks and Communications
- Information Systems
- Signal Processing