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from Part Three - Compressive Sensing
Published online by Cambridge University Press: 21 April 2022
This chapter returns to the recovery of sparse vectors, but this time the linear measurements are quantized to retain only their signs. With the help of the restricted isometry property from ?2 to ?1, it is shown that the direction of sparse vectors can still be approximately recovered via a hard thresholding procedure or via a linear program. Furthermore, it is shown that the magnitude, too, can be recovered if an appropriate modification of the signed observations is allowed.
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