Statistics and Its Interface

Volume 6 (2013)

Number 1

Assessment of random-noise contamination in digital images via testing on wavelet coefficients

Pages: 117 – 135



Diego Maldonado (Department of Mathematics, Kansas State University, Manhattan, Ks., U.S.A.)

Sharad Silwal (Northland College, Ashland, Wisconsin, U.S.A.)

Haiyan Wang (Department of Statistics, Kansas State University, Manhattan, Ks., U.S.A.)


Full-reference image quality assessment methods seek to measure visual similarity between two images (in practice, one original and the other its altered version). It has been established that traditional methods, such as Mean Square Error and Peak Signal-to-Noise Ratio poorly mimic the human visual system and much of the recent research in image quality assessment has been directed toward developing image similarity measures that are more consistent with assessments from human observers. Some extensively tested popular methods in this regard are Visual Image Fidelity (VIF), Structure Similarity Index (SSIM) and its variants Multi-scale Structure Similarity Index (MS-SSIM) and Information Content Weighted Multi-scale Structure Similarity Index (IW-SSIM). However, experiments show that these methods may produce drastically different similarity indices for different images contaminated with the same source of random noise. In this article, we propose a new full-reference image quality assessment method, namely, Wavelet-based Non-parametric Structure Similarity Index (WNPSSIM), specifically designed to detect visual similarity between images contaminated with all sorts of random noises. WNPSSIM is based on a rank test of the hypothesis of identical images conducted on the wavelet domain. Our experimental comparisons demonstrate that WNPSSIM provides similar ranking as MS-SSIM, IW-SSIM and VIF for images contaminated with different random noises in general though the methodology is very different. In addition, WNPSSIM corrects the aforementioned shortcoming of assigning sharply different similarity indices for different images contaminated with the same source of random noise.


image structure similarity, nonparametric hypothesis testing, full-reference, human visual system (HVS), discrete wavelet transform (DWT)

2010 Mathematics Subject Classification

Primary 62H35, 68U10, 97K80. Secondary 62G10.

Published 18 March 2013