A Multidimensional Companding Scheme for Source Coding with a Perceptually Relevant Distortion Measure

In this paper, we develop a multidimensional companding scheme for the preceptual distortion measure by S. van de Par [1]. The scheme is asymptotically optimal in the sense that it has a vanishing rate-loss with increasing vector dimension. The compressor operates in the frequency domain: in its simplest form, it pointwise multiplies the Discrete Fourier Transform (DFT) of the windowed input signal by the square-root of the inverse of the masking threshold, and then goes back into the time domain with the inverse DFT. The expander is based on numerical methods: we do one iteration in a fixedpoint equation, and then we fine-tune the result using Broyden’s method. Additionally, we will show simulations which corroborate the approximations and results of the theoretical derivations.