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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: This paper attempts to link sparse optimization methodology to the anatomical structure of locust's early olfactory system. The work is motivated by the observation that odorant molecules are sparsely represented by the population of Kenyon cells. The authors first mathematically formulate the olfactory system as a MAP decoder, and give the standard solution to the problem without considering biological constraints. Next, to make the solution more biologically plausible, the authors reformulate the olfactory system model as a decoder of a compressive sensing problem, and provide two standard solutions to the dual problem. Then, the authors argue that each of the components in the solution can be mapped/interpreted to/as a unit of the biological structure in the olfactory system. However, these maps are described without a strong justification and there are conceptual problems in linking the math with the biology.