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- Maskan, Hoomaan, et al.
(författare)
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A Variational Perspective on High-Resolution ODEs
- 2023
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Ingår i: Advances in Neural Information Processing Systems 36 (NeurIPS 2023). - : Neural information processing systems foundation.
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Konferensbidrag (refereegranskat)abstract
- We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence rate for gradient norm minimization using Nesterov's accelerated gradient method. Additionally, we show that Nesterov's method can be interpreted as a rate-matching discretization of an appropriately chosen high-resolution ODE. Finally, using the results from the new variational perspective, we propose a stochastic method for noisy gradients. Several numerical experiments compare and illustrate our stochastic algorithm with state of the art methods.
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| 2. |
- Maskan, Hoomaan, et al.
(författare)
-
Demixing sines and spikes using multiple measurement vectors
- 2023
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Ingår i: Signal Processing. - : Elsevier. - 0165-1684 .- 1872-7557. ; 203
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Tidskriftsartikel (refereegranskat)abstract
- We address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the measurements can be modeled as the sum of a spectrally sparse and a block-sparse signal known as outlier. Our aim is to demix the two components and for this purpose, we design a convex problem whose objective function promotes both of the structures. Using the Positive Trigonometric Polynomials (PTP) theory, we reformulate the dual problem as a Semidefinite Program (SDP). Our theoretical results state that for a fixed number of measurements N and constant number of outliers, up to O(N) spectral lines can be recovered using our SDP problem as long as a minimum frequency separation condition is satisfied. Our simulation results also show that increasing the number of samples per measurement vectors reduces the minimum required frequency separation for successful recovery.
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