The paper presents and evaluates a speckle detection method for B-scan images. This is a fully automatic method and does not require information about the sensor parameters, which is often missing in retrospective studies. The characterization and posterior detection of speckle noise in ultrasound (US) has been regarded as an important research topic in US imaging, for improving signal-to-noise ratio by removing speckle noise and for exploiting speckle correlation information. Most of the existing methods require either manual intervention, the need to know sensor parameters or are based on statistical models which often do not generalize well to B-scans of different imaging areas. The proposed method aims to overcome those limitations. The main novelty of this work is to show that speckle detection can be improved based on finding optimally discriminant low order speckle statistics. In addition, and in contrast with other approaches the presented method is fully automatic and can be efficiently implemented to B-scan images. The method detects speckle patches using an ellipsoid discriminant function which classifies patches based on features extracted from optimally discriminant low order moments of the uncompressed intensity B-scan information. In addition, if the uncompressed signal is not available, we propose and evaluate a method for the estimation of this factor. The computation of low order moments using an optimality criteria, the decompression factor estimation and other key aspects of the method are quantitatively evaluated using both simulated and real (phantom and in vivo) data. Speckle detection results are obtained using again phantom and in vivo studies which show the validity of our approach. In addition, speckle probability images (SPI) are presented which provide valuable information about the distribution of speckle and non-speckle areas in an image. The presented evaluation and results show the effectiveness of our approach. In particular, the need for using discriminant analysis to determine the optimal discriminant power of the statistical moments and that this optimal value strongly depends on the characteristics and imaged tissues in the B-scan data.