Quantitative evaluation of image information retention by relative phases

Phase only reconstructed images are indispensable for image understanding and processing nowadays. A few domain transforms like Fourier transform provide absolute phase while others like complex wavelet, curvelet etc. give relative phase. It is well known that absolute phase contains most of the information embedded in an image. However, limited attempts have been made to investigate the information contributed by the relative phase. This paper analyzes the ability to extract the image information by relative phase quantitatively. Three indices based on structural similarity, dependency, and mutual information between original and phase only reconstructed images have been proposed to quantify the information retentivity. The structural similarity (SSIM) index, correlation coefficient, and mutual information determined by Shannon entropy (MISE) and that by Renyi entropy (MIRE) are adopted to compare the performances of relative phases given by complex wavelet and curvelet transforms on various image database. Experimental evaluation demonstrates the potentiality of relative phase for extraction of image information and aids to select the most informative phase only reconstruction method in different applications.