Abstract:

Frame coefficients of a d-dimensional signal x represent x perfectly, since we can reconstruct x exactly from these coefficients. Generally frame coefficients are arbitrary real or complex numbers. However, many digital signal processing applications require digital data. In digital applications, a finite alphabet of numbers is specified, and each component of a datum is represented with a number in this alphabet. The frame quantization problem is the problem of finding a frame expansion x' with coefficients coming from a fixed alphabet, such that x' is close to x in some prescribed way.

In this talk, first, we make a signal-wise comparison of two industry standards of quantization, Pulse Code Modulation (PCM) and Sigma-Delta quantization, in the context of finite frames. Second, we propose two new quantization methods for finite frame expansions.