Minimization of errors in L4−norm for decoding quantized data: its application to quantization of wavelet coefficients

Two well known quantization methods are uniform quantization and Max–Lloyd. We present a novel quantization method, based on minimizing the L4−norm of the errors. This method has a performance superior to uniform quantization and Max–Lloyd when applied directly to an image, and is superior to Max–Lloyd when applied to the coefficients of a wavelet transform. We make various tests, we give an insight to the behaviour of the methods and prove our statement in a simple case. We generalize our method and conjecture upon the performance of all quantizers minimizing the Lp−norm of the errors.