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- W4289713091 abstract "A universal 1-bit compressive sensing (CS) scheme consists of a measurement matrix A such that for all signals x belonging to a particular class, x can be approximately recovered from sign(Ax). 1-bit CS models extreme quantization effects where only one bit of information is revealed per measurement. We focus on universal support recovery for 1-bit CS in the case of sparse signals with bounded dynamic range. Specifically, a vector x ∈ℝ <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sup> is said to have sparsity k if it has at most k nonzero entries and dynamic range R if the ratio between its largest and smallest nonzero entries is at most R in magnitude. Our main result shows that if the entries of the measurement matrix Ax are i.i.d. Gaussians, then the number of measurements needs to be ${{tilde Omega }}left({R{k^{3/2}}}right)$ to recover the support of k-sparse signals with dynamic range R using 1-bit CS. This contrasts with the known lower bound of ${{tilde Omega }}left({{k^2}log n}right)$ for the number of measurements to recover the support of arbitrary k-sparse signals. In broad scaling regimes of interest, our lower bounds match upper bounds implicit in prior works up to logarithmic factors." @default.
- W4289713091 created "2022-08-04" @default.
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- W4289713091 date "2022-06-26" @default.
- W4289713091 modified "2023-10-14" @default.
- W4289713091 title "Universal 1-Bit Compressive Sensing for Bounded Dynamic Range Signals" @default.
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- W4289713091 doi "https://doi.org/10.1109/isit50566.2022.9834417" @default.
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