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We develop new multiscale amplitude-modulation frequency-modulation (AM-FM) demodulation methods for image processing. The approach is based on three basic ideas: (i) AM-FM demodulation using a new multiscale filterbank, (ii) new, accurate methods for instantaneous frequency (IF) estimation, and (iii) multiscale least squares AM-FM reconstructions. In particular, we introduce a variable-spacing local linear phase (VS-LLP) method for improved instantaneous frequency (IF) estimation and compare it to an extended quasilocal method and the quasi-eigen function approximation (QEA). It turns out that the new VS-LLP method is a generalization of the QEA method where we choose the best integer spacing between the samples to adapt as a function of frequency. We also introduce a new quasi-local method (QLM) for IF and IA estimation and discuss some of its advantages and limitations. The new IF estimation methods lead to significantly improved estimates. We present different multiscale decompositions to show that the proposed methods can be used to reconstruct and analyze general images.