In end-to-end learned image compression, encoder and decoder are jointly trained to minimize a $R + λD$ cost function, where $λ$ controls the trade-off between rate of the quantized latent representation and image quality. Unfortunately, a distinct encoder-decoder pair with millions of parameters must be trained for each $λ$, hence the need to switch encoders and to store multiple encoders and decoders on the user device for every target rate. This paper proposes to exploit a differentiable quantizer designed around a parametric sum of hyperbolic tangents, called STanH , that relaxes the step-wise quantization function. STanH is implemented as a differentiable activation layer with learnable quantization parameters that can be plugged into a pre-trained fixed rate model and refined to achieve different target bitrates. Experimental results show that our method enables variable rate coding with comparable efficiency to the state-of-the-art, yet with significant savings in terms of ease of deployment, training time, and storage costs

Submitted to IEEE Transactions on Image Processing