Phase-only image synthesis using Fast Generalized Fourier Family Transform (FGFT)

Abstract

The phase components of complex valued transform coefficients retain the edge information of an image. Fast Generalized Fourier Transform (FGFT) is a complex, non-redundant, progressive resolution, globally referenced phase output, time-frequency representation applicable for non-stationary signals. Though the analysis of forward FGFT framework for 1D signal is present in literature, analysis of synthesis (or reverse) FGFT framework is not available for 1D and 2D signals. An Image (2D signal) synthesized using only phase components of FGFT, does not produce edge information. In the process of FGFT, Fourier Transform (FT) phase coefficients gets mingled together, thus the normalization procedure used to retain phase is ineffective to separate FT phase coefficients from FGFT samples. This thesis proposes an algorithm to effectively separate FT phase coefficients from FGFT samples and thus reconstruct image with edge information from phase-only components of FGFT samples. The amount of information present in phase and magnitude of different transforms is measured. The comparison indicates that FT retains most information than others in phase-only image reconstruction and Curvelet Transform (CT) retains most information in magnitude-only image reconstruction compared to other transforms. In contrast, FGFT retains edge information equally in both magnitude and phase components.