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
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