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. Author manuscript; available in PMC: 2019 Feb 15.
Published in final edited form as: IEEE Trans Signal Process. 2017 Nov 20;66(4):1037–1050. doi: 10.1109/TSP.2017.2775591

Algorithm 1.

Outline of the invariant approach for MRA

Input: Set of observations ξj, j = 1, …, M according to (I.1) and noise level σ
Output: x̂: estimation of x
Estimate invariant features:

  1. Compute μ̂x according to (II.2)

  2. Compute P̂x according to (II.4)

  3. Compute B̂x−μx according to (II.8)

Estimate the signal’s DFT:

  1. Estimate y[0] from μ̂x. For other frequencies:

  2. Estimate the magnitudes of y from P̂x

  3. Estimate the phases of y from B̂x−μx (e.g., Algorithm 2)

Return: x̂: inverse DFT of the estimated y