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State-of-the-art lossless image compression schemes, such as JPEG-LS and CALIC, have been proposed in the context-adaptive predictive coding framework. These schemes involve a prediction step followed by context-adaptive entropy coding of the residuals. However, the models for context determination proposed in the literature, have been designed using ad-hoc techniques. In this paper, we take an alternative approach where we fix a simpler context model and then rely on a systematic technique to efficiently exploit spatial correlation to achieve efficient compression. The essential idea is to decompose the image into binary bitmaps such that the spatial correlation that exists among non-binary symbols is captured as the correlation among few bit positions. The proposed scheme then encodes the bitmaps in a particular order based on the simple context model. However, instead of encoding a bitmap as a whole, we partition it into rectangular blocks, induced by a binary tree, and then independently encode the blocks. The motivation for partitioning is to explicitly identify the blocks within which the statistical correlation remains the same. On a set of standard test images, the proposed scheme, using the same predictor as JPEG-LS, achieved an overall bit-rate saving of 1.56% against JPEG-LS.