Nonstationary Gabor Frames - Approximately Dual Frames and\n Reconstruction Errors

2013/01/09 by Monika Dörfler, Dörfler, Monika, Ewa Matusiak +1
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Photoacoustic and Ultrasonic Imaging #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1301.1802

openalex publication_date 2013/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nonstationary Gabor frames, recently introduced in adaptive signal analysis,\nrepresent a natural generalization of classical Gabor frames by allowing for\nadaptivity of windows and lattice in either time or frequency. Due to the lack\nof a complete lattice structure, perfect reconstruction is in general not\nfeasible from coefficients obtained from nonstationary Gabor frames. In this\npaper it is shown that for nonstationary Gabor frames that are related to some\nknown frames for which dual frames can be computed, good approximate\nreconstruction can be achieved by resorting to approximately dual frames. In\nparticular, we give constructive examples for so-called almost painless\nnonstationary frames, that is, frames that are closely related to nonstationary\nframes with compactly supported windows. The theoretical results are\nillustrated by concrete computational and numerical examples.\n

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