Adaptive Dictionary Sparse Signal Recovery Using Binary Measurements
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One-bit compressive sensing is an extended version of compressed sensing in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measurement is available to us. There exist may practical application in which the underlying signal is not sparse directly, but it can be represented in a redundant dictionary. Apart from that, one can refine the sampling procedure by using profitable information lying in previous samples. this information can be employed to reduce the required number of measurements for exact recovery by adaptive sampling schemes. In this work, we proposed an adaptive algorithm that exploits the available information in previous samples. The proof uses the recent geometric concepts in high dimensional estimation. we show through rigorous and numerical analysis that our algorithm considerably outperforms non-adaptive approaches. Further, it reaches the optimal error rate from quantized measurements.
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