A Nonlinear Reconstruction Algorithm from Absolute Value of Frame Coefficients for Low Redundancy Frames. Radu Balan University of Maryland College Park, MD 208742 email: [email protected] SampTA 2009 - Marseille, France. Statement of the Problem . H=E n , where E= R or E= C
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University of Maryland
College Park, MD 208742
email: [email protected]
SampTA 2009 - Marseille, France
is injective up to a constant phase factor ambiguity
Very thin layer, so that r is 2-D
Given I(k) , estimate R(r).
Theorem [R.B.,Casazza, Edidin, ACHA(2006)]
whereas we know that m=O(n) should be sufficient.
This paper presents a novel algorithm that interpolates between O(n) and O(n2) keeping similar properties to the previous algorithm.
(E requires a high redundancy.n)
Necessary Condition for Linear Reconstruction:
Real Case: requires a high redundancy.E=R
is satisfied for
Note the critical case
Complex Case: requires a high redundancy.E=C
is satisfied by the following (suboptimal) choice
but larger than 4n-2
is generically spanning in Ed.