Georgia Institute of Technology College of Sciences

Consistent reconstruction is a method for estimating a signal from a collection of noisy linear measurements that are corrupted by uniform noise. This problem arises, for example, in analog-to-digital conversion under the uniform noise model for memoryless scalar quantization. We shall give an overview of consistent reconstruction and prove optimal mean squared error bounds for the quality of approximation. We shall also discuss an iterative alternative (due to Rangan and Goyal) to consistent reconstruction which is also able to achieve optimal mean squared error; this is closely related to the classical Kaczmarz algorithm and provides a simple example of the power of randomization in numerical algorithms.