Localized phase is extracted from images represented in the combined frequency- position space. It is shown that images represented by localized phase-only information reproduce adequately the edge relationship while compressing the gray level information, unlike the localized magnitude-only representation that distorts the edge information. We address the issue of the number of quantization levels required for adequate representation by localized phase, and present an analytical expression of the resultant image as well as computational examples. We show that image reconstruction from localized phase-only is more efficient than image reconstruction from global (Fourier) phase in that the number of required computer operations is reduced and the rate of convergence is improved. The computation efficiency can be further improved by implementation of highly- parallel architecture.