Abstract: A method and apparatus for adaptive bit allocation and hybrid lossless entropy encoding in a lossy compression system. The invention includes three components: (1) a transform stage to decorrelate image data into a baseband and multiple subbands, (2) a quantization stage to quantize the resulting transform coefficients, and (3) a lossless entropy coder stage to encode the quantized indexes. In the preferred embodiment, the transform stage uses a wavelet transform algorithm. The quantization stage adaptively estimates values for parameters defining an approximation between quantization size and the logarithm of quantization error, and recursively calculates the optimal quantization size for each band to achieve a desired bit rate. The baseband and subbands are transformed into quantization matrices using the corresponding quantization sizes.