Portraits of frames: overcomplete representations with applications to image processing

Akram Aldroubi

doi:10.1117/12.162073

1 November 1993 Portraits of frames: overcomplete representations with applications to image processing

Akram Aldroubi

Proceedings Volume 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing; (1993) https://doi.org/10.1117/12.162073
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

We present two methods for generating frames of a Hilbert space H. The first method uses bounded operators on H to transform a frame into another frame of H₁ C H. The other method uses bounded linear operators on l₂ to generate frames of H. We characterize all the mappings that transform frames into other frames. We also show how to construct all frames of a given Hilbert space H starting from any given frame. We show how to apply the theory to obtain shift-invariant tight frames, and shift-invariant tight multiresolution. We also show how to obtain scaling function and wavelets with prescribed properties. Finally, we discuss the noise reduction properties of frames.

Citation Download Citation

Akram Aldroubi "Portraits of frames: overcomplete representations with applications to image processing", Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); https://doi.org/10.1117/12.162073

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