Pattern Analysis & Applications (2000)3:303–313  2000 Springer-Verlag London Limited Using Renyi’s Information and Wavelets for Target Detection: An Application to Mammograms G. Boccignone 1 , A. Chianese 2 and A. Picariello 2 1 DIIIE and INFM, Universita` di Salerno, Fisciano, Italy; 2 DIS, Universita` di Napoli, Napoli, Italy Abstract: In this paper we present a multi-scale method for the detection of small targets embedded in noisy background. The multi- scale representation is built using a weighted undecimated discrete wavelet transform. The method, in essence, is based on the maximisation of information available at each resolution level of the representation. We show that such objective can be achieved by maximising Renyi’s information. This approach allows us to determine an adaptive threshold useful for discriminating, at each scale, between wavelet coefficients representing targets and those representing background noise. Eventually, avoiding inverse transformation, scale-dependent estimates are combined according to a majority vote strategy. The proposed technique is experimented on a standard data set of mammographic images. Keywords: Mammograms; Medical imaging; Multi-resolution; Renyi’s information; Scale-space; Target detection; Wavelet transform 1. INTRODUCTION The problem of detecting targets through their automatic spatial localisation in a noisy background is of interest to several realms such as medical imaging, multispectral sensing, pattern recognition and information theory [1]. Generic targets exhibit a great variability of shape and appearance, scale and orientation, lighting and imaging conditions and natural background clutter. To address generic target detec- tion, any method should in principle be powerful enough to cope with all such controversial features. Yet, it would be necessary to circumscribe the generality of these features by exploiting knowledge of the underlying nature of the world in which targets are generated and observed [2]. In practice, current research in this area is mainly dealing with algorithms relying on various restrictions on the applications. In this work, we study the detection of small targets embedded within an inhomogeneous, textured background, and we assume that no other contextual knowledge is either taken into account or available. To be more precise, by detection we mean the spatial localisation of the targets, Received: 29 June 1999 Received in revised form: 28 January 2000 Accepted: 28 January 2000 not being concerned with their exact shape reconstruction. To make progress, if we are not interested in gauging the structure of the background, the latter can be handled as an obscuring signal or ‘noise’. Under this assumption, the target detection can be reformulated as a problem of signal/noise discrimination. This is generally known as de- noising problem: given an image, a finite energy function, I  L 2 (R 2 ), the detection process can be expressed as an estimation problem of the ‘true’ but unknown signal I  (the target), hidden by a background ‘noise’ I  , from the observed data I: I(x,y) = I  (x,y)+ I  (x,y) (1) where (x,y) is a point of the image domain. Advanced statistical methods have been developed for this problem, from basically two different perspectives [1]. A first class of methods assumes prior knowledge to be available, and bayesian estimates are computed for the unknown signal. Such estimates are optimal under the ‘true’ model, but unfortunately, such a model is seldom if not at all available in practice. Then, non-parametric estimation methods often provide an appealing alternative. Clearly, if we do not take into account any prior know- ledge, the amount of information at hand is merely a function of the signal-to-noise ratio. On the other hand, in