Many significant features of images are represented in their Fourier transform. The spectral phase of an image can often be measured more precisely than magnitude for frequencies of up to a few GHz. However, spectral magnitude is the only measurable data in many imaging applications. In this paper, the reconstruction of complex-valued images from either the phases or magnitudes of their Fourier transform is addressed. Conditions for unique representation of a complex-valued image by its spectral magnitude combined with additional spatial information is investigated and presented. Reconstruction algorithms of complex-valued images are developed and introduced. Three types of reconstruction algorithms are presented. (1) Algorithms that reconstruct a complex-valued image from the magnitude of its discrete Fourier transform and part of its spatial samples based on the autocorrelation function. (2) Iterative algorithms based on the Gerchberg and Saxton approach. (3) Algorithms that reconstruct a complex-valued image from its localized Fourier transform magnitude. The advantages of the proposed algorithms over the presently available approaches are presented and discussed.
We introduce a new approach to video compression based on the Discrete Cosine Transform (DCT) generalized to 3 dimensions. An efficient tool of 'Activity Map' further exploits the temporal redundancies of video sequences, providing a very-low bit-rate system. The result is a compression ratio of more than 150:1 with good quality of the reconstructed sequence, measured as more than 37 db (PSNR). Although the compression results are comparable with existing methods, such as MPEG or H.263, the complexity of the proposed approach is approximately 90% lower, making it suitable for hand-held systems such as cellular videophones.
The Gram determinant technique is applied to signal representation by non-orthogonal bases. A special case of image representation in biological and machine vision using Gabor elementary functions (GEFs) is considered. It is shown that, in general, the Gram determinant is a better approach to computation of the expansion coefficients than the one using bi-orthonormal auxiliary functions. An optimal representation by finite sets of coefficients is attained without a significant computational effort and the resultant reconstruction error converges monotonically with the addition of basis’ components to the reconstruction set. The Gram approach appears to be in a better accord with biological findings, regarding information processing along the visual pathway, compared to the conventional bi-orthogonal scheme.