The paper presents a universal statistical model for texture images based on an overcomplete complex wavelet transform. The model is parameterized by statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. An efficient algorithm is developed to synthesize random images subject to these constraints, and the model's perceptual validity is tested through examples that fail when certain parameters are removed. The model's power is demonstrated by successfully synthesizing a diverse collection of artificial and natural textures. The paper also re-examines the Julesz conjecture, which hypothesizes that a set of functions can partition textures into classes that are visually indistinguishable, and shows that the proposed model provides a more robust and flexible approach to texture modeling.The paper presents a universal statistical model for texture images based on an overcomplete complex wavelet transform. The model is parameterized by statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. An efficient algorithm is developed to synthesize random images subject to these constraints, and the model's perceptual validity is tested through examples that fail when certain parameters are removed. The model's power is demonstrated by successfully synthesizing a diverse collection of artificial and natural textures. The paper also re-examines the Julesz conjecture, which hypothesizes that a set of functions can partition textures into classes that are visually indistinguishable, and shows that the proposed model provides a more robust and flexible approach to texture modeling.