Compressed sensing is now established as an effective method for dimensionreduction when the underlying signals are sparse or compressible with respectto some suitable basis or frame. One important, yet under-addressed problemregarding the compressive acquisition of analog signals is how to performquantization. This is directly related to the important issues of how"compressed" compressed sensing is (in terms of the total number of bits oneends up using after acquiring the signal) and ultimately whether compressedsensing can be used to obtain compressed representations of suitable signals.Building on our recent work, we propose a concrete and practicable method forperforming "analog-to-information conversion". Following a compressive signalacquisition stage, the proposed method consists of a quantization stage, basedon $\Sigma\Delta$ (sigma-delta) quantization, and a subsequent encoding(compression) stage that fits within the framework of compressed sensingseamlessly. We prove that, using this method, we can convert analog compressivesamples to compressed digital bitstreams and decode using tractable algorithmsbased on convex optimization. We prove that the proposed AIC provides a nearlyoptimal encoding of sparse and compressible signals. Finally, we presentnumerical experiments illustrating the effectiveness of the proposedanalog-to-information converter.
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