We propose a new adaptive block-wise lossless image compression algorithm, which is based on the so-called alphabet reduction scheme combined with an adaptive arithmetic coding (AC). This new encoding algorithm is particularly efficient for lossless compression of images with sparse and locally sparse histograms. AC is a very efficient technique for lossless data compression and produces a rate that is close to the entropy; however, a compression performance loss occurs when encoding images or blocks with a limited number of active symbols by comparison with the number of symbols in the nominal alphabet, which consists in the amplification of the zero frequency problem. Generally, most methods add one to the frequency count of each symbol from the nominal alphabet, which leads to a statistical model distortion, and therefore reduces the efficiency of the AC. The aim of this work is to overcome this drawback by assigning to each image block the smallest possible set including all the existing symbols called active symbols. This is an alternative of using the nominal alphabet when applying the conventional arithmetic encoders. We show experimentally that the proposed method outperforms several lossless image compression encoders and standards including the conventional arithmetic encoders, JPEG2000, and JPEG-LS.