Reconstruction of Algebraic-exponential Data from Moments and Solving a Generalized Lowner-John Prob

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Claims exact recovery of algebraic–exponential functions from a finite moment sequence up to order 2d by checking a rank condition on the moment matrix and solving a concrete convex program. Uses moment matrices, polynomial identities and semidefinite relaxation to turn reconstruction into an SDP that outputs coefficients and support parameters. Applies a similar convex formulation to a generalized Lowner–John minimal-volume problem and demonstrates exact recovery on synthetic examples and stability under small Gaussian noise.

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1. 0:00Start
2. 3:30Exact reconstruction
3. 4:09Exact recovery (continued)
4. 7:27A little detour
5. 9:36Some motivation
6. 16:29Proof for nonnegative
7. 18:18An alternative proof
8. 19:41II. Approximating a non gaussian integral
9. 21:28III. Convexity
10. 22:29Convexity (continued)
11. 24:20Polarity (continued)
12. 25:06IV. A variational property of homogeneous polynomials
13. 36:02VI. Recovering g from moments of G
14. 39:10Non homogeneous polynomials
15. 47:09Sketch of the proof
16. 51:15Conclusion
17. 52:02Some references