In this thesis, for the application of progressive lossless image coding and transmission, we proposed a new image interpolation algorithm called Edge Adaptive Hierarchical INTerpolation (EAHINT). We compute the local variance of the causal context to model the strength of a local edge around a target pixel and then apply three statistical decision rules to classify the local edge into a strong edge, a weak edge, or a medium edge. According to these local edge types, we apply an interpolation method to the target pixel using a one-directional interpolator for a strong edge, a multi-directional adaptive weighting interpolator for a medium edge, or a non-directional static weighting linear interpolator for a weak edge. Experimental results show that the proposed algorithm achieves a better compression bit rate than the New Interleaved Hierarchical Interpolation (NIHINT) method, which is recognized as a superior pyramid data structure for progressive lossless image compression and transmission. Experimental results show that the compression bit rate is much better for images that are rich in directional edges and textures. Our algorithm also shows better rate-distortion performance and visual quality in progressive image transmission.