Processes for compressing images with sparse histograms are disclosed. The image is divided into blocks, and a bit budget is assigned for each block. The pixels of a block are converted and coded bit-plane by bit-plane, starting from the Most Significant Bit (MSB) and going towards the Least Significant Bit (LSB). The pixels of the block are partitioned into groups. Each group contains pixels that have same value. Moving from the MSB to the LSB, the groups in each bit-plane are processed. When processing a group, the encoder sends a “0” if all group members have same bit value at the current bit-plane being processed, followed by the bit value; otherwise, the encoder sends a “1”, followed by refinement bits for each pixel of the group, and the encoder splits the group.