Quaternionic wavelet coefficients modeling for a Reduced-Reference metric

• Description of Quaternionic Wavelet Transform (QWT) and Information Criteria (IC).
• Proposition of a probability density function (PDF) for each QWT features.
• Reference image’s PDF and the distributions of degraded image are compared.
• QWT’s shift invariant magnitude provides information to describe the degradation.
• QWT’s structural phase completes structure analysis and is seen as a texture feature.
• Proposed metric gives better prediction (accuracy and monotonicity) than RRIQA.
• RRIQA is the most Reduced-Reference measure used in the image processing literature.
• Proposed metric remains competitive against several classical Full-Reference metrics.

This paper proposes a new Reduced-Reference metric based on the modeling of the Quaternionic Wavelet Transform coefficients from Information Criteria. To obtain the Reduced-References, we will model the Quaternionic Wavelet Transform coefficients using probability density functions whose parameters are used as Reduced-References. Information Criteria are proposed in order to build optimal histograms of the Quaternionic Wavelet Transform coefficients and to obtain the number of distributions in the mixture model. The Quaternionic Wavelet Transform is an improvement of the Discrete Wavelet Transform providing a richer scale-space analysis for 2-D signals. This recent transform separates the information contained in the image better than a classical Discrete Wavelet Transform, and provides a multiscale image analysis whose coefficients are 2D analytic, with one near-shift invariant magnitude and with phase information. From these models, we propose a measure of degradation by comparing probability density functions of the reference image and the distributions of the degraded image of the Quaternionic Wavelet Transform subbands. We shall demonstrate that one phase of the Quaternionic Wavelet Transform provides relevant information in the Image Quality Assessment. Experimentation confirmed the potential of this new structural information (this Reduced-Reference system produces good coefficients of correlation with the Human Visual System).