2011 # Left Invariant Evolution Equations on Gabor Transforms

**Abstract:** By means of the unitary Gabor transform one can relate operators on signals to operators on the space of Gabor transforms. In order to obtain a translation and modulation invariant operator on the space of signals, the corresponding operator on the reproducing kernel space of Gabor transforms must be left invariant, i.e. it should commute with the left regular action of the reduced Heisenberg group H r . By using the left invariant vector fields on H r and the corresponding left-invariant vector fields on on p…

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“…For details on phase covariant diffusions on Gabor transforms (see the right column in Fig. 8.1), we refer to [118,Chap. 7] and [236,Chap.…”

confidence: 99%

“…For details on phase covariant diffusions on Gabor transforms (see the right column in Fig. 8.1), we refer to [118,Chap. 7] and [236,Chap.…”

confidence: 99%

“…This however does not imply that it is a redundant direction in the group manifold H r itself, since clearly the s-axis represents the relevant phase and stores the noncommutative nature between position and frequency, [118,Chap. 1].…”

confidence: 99%

“…[58,20], However, strain can also be directly computed from frequency fields using (enhanced) Gabor transforms, cf. [13].…”

confidence: 99%