In this talk, I will describe a new scheme for successively refinable lossy compression.

In each iteration, the encoder merely describes the indices of the few maximal source components,

while the decoder’s reconstruction is a natural estimate of the source components

based on this information. This step can be shown to be near-optimal for the memoryless

Gaussian source in the sense of achieving the zero-rate slope of its distortion-rate function.

I will then introduce a scheme comprising of iterating the above iteration on an appropriately

transformed version of the difference between the source and its reconstruction from the previous iteration.

The proposed scheme achieves the rate distortion function of the Gaussian memoryless source (under squared error distortion) when employed

on any finite-variance ergodic source. Its storage and computation requirements are modest

at both the encoder and decoder. It further possesses desirable properties which I will discuss, which

we respectively refer to as infinitesimal successive refinability, ratelessness, and complete separability.

Our work provides new insights regarding video and image compression

as well as bio data compression such as genomic data.

Based on joint work with Tsachy Weissman.