## 1 Introduction  
Mammography is currently the best radiological technique for early detection of breast cancer. An efficient and robust algorithm has been developed to process digitized and/or digital X-ray mammographic images in order to detect subtle abnormalities, such as different kind of lesions (e.g., microcalcifications, opacities or stellate patterns of straight lines), which may indicate the presence of malignancies. The study is intended to improve the diagnosis of mammographic lesions by using computer image analysis methods to derive quantitative description of their visual characteristics like edge definition, extent, and texture. Though experienced radiologists may often establish the malignant or benign nature of a lesion on the basis of these characteristics, the image perception by human observers is subject to complex interpretation by the visual system. The consequence is that the perceived image does not always correspond to the actual data contained in the image, which might lead to inaccurate or incorrect conclusions [1]. Irrespective of their sophistication and diversity, the numerical methods commonly used to convert experimental data into interpretable images and spectra rely on straightforward transforms, such as the Fourier transform (FT) or quite elaborated emerging classes of transforms like wavelets [2, 3], wedgelets [4], ridgelets [5], and so forth. Implemented by its version known as fast Fourier transform (FFT), the widely spread FT is a an efficient and convenient means of converting time domain data into frequency domain spectra. Moreover, the FFT is linear, so that the relative intensities of resonances of different widths, shapes, and frequencies are not distorted, and it is model-free. Yet experimental data are incomplete and noisy due to the limiting constraints of digital data recording and the finite acquisition time. The pitfall of most transforms is that imperfect data are directly transferred into the transform domain along with the signals of interest. The traditional approach to data processing in the transform domain is to ignore any imperfections in data, set to zero any unmeasured data points, and then proceed as if data were perfect. Contrarily, the maximum entropy (ME) principle enforces data processing in space (time) domain [6]. In data analysis, the ME methods are primarily used to reconstruct positive distributions, such as images and spectra, from blurred, noisy, and/or corrupted data. The ME methods may be developed on axiomatic foundations based on the probability calculus that has a special status as the only internally consistent language of inference [7, 8]. Within its framework, positive distributions ought to be assigned probabilities derived from their entropy. Measurements on a complete collection of images, which correspond to all possible intensity distributions, act as a filter by restricting the focus on the images that satisfy the acquired data with noise. Among these, a natural choice may be the one that could have arisen in the maximum number of ways, depending on some counting rule. Such an approach to statistical inference was first suggested by [PERSON] [9] and completed by [PERSON] [10]. Bayesian statistics provides a unifying and self-consistent framework for data modeling. Bayesian inference naturally deals with uncertainty in data explained by marginalization in predictions of other variables. Data overfitting and poor generalization are alleviated by incorporating the principle of Occam's razor, which controls model complexity and sets the preference for simpler models [12]. Bayesian inference satisfies the likelihood principle [13] in the sense that inferences depend only on the probabilities assigned to data that were measured and not on the properties of some admissible data that were never acquired. As such, out of all images that satisfy the measurements, the entropic restoration corresponds to selecting the most probable individual one that maximizes a given measure of entropy.