Improved Reversible Mapping from Color to Gray

In the reversible conversion of color images to gray ones, colors are mapped to textures and from the textures the receiver can recover the colors, i.e. one may print a color image with a black and white printer and, at a later time, recover colors. Such a method was originally devised using the wavelet transform and replacing high-frequency subbands by subsampled chrominance planes. Here, we propose to improve the original method thorough the use of a largely redundant representation of the chrominance, with multiple embedding into subbands of a general subband transform. Our results point to minimization of the variance of the error caused by noise when the chrominance is replicated into many subbands and not linearly combined. Derived noise bounds guide us on how many subbands to embed the chrominance. Experimental results were carried for multiple noise levels, models, transform sizes, and number of embedding subbands, demonstrating the theoretical analysis and the method's potential.