Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constrained adaptive sensing   Suppose that we wish to estimate a vector $\mathbf{x} \in \mathbb{C}^n$ from
a small number of noisy linear measurements of the form $\mathbf{y} = \mathbf{A
x} + \mathbf{z}$, where $\mathbf{z}$ represents measurement noise. When the
vector $\mathbf{x}$ is sparse, meaning that it has only $s$ nonzeros with $s
\ll n$, one can obtain a significantly more accurate estimate of $\mathbf{x}$
by adaptively selecting the rows of $\mathbf{A}$ based on the previous
measurements provided that the signal-to-noise ratio (SNR) is sufficiently
large. In this paper we consider the case where we wish to realize the
potential of adaptivity but where the rows of $\mathbf{A}$ are subject to
physical constraints. In particular, we examine the case where the rows of
$\mathbf{A}$ are constrained to belong to a finite set of allowable measurement
vectors. We demonstrate both the limitations and advantages of adaptive sensing
in this constrained setting. We prove that for certain measurement ensembles,
the benefits offered by adaptive designs fall far short of the improvements
that are possible in the unconstrained adaptive setting. On the other hand, we
also provide both theoretical and empirical evidence that in some scenarios
adaptivity does still result in substantial improvements even in the
constrained setting. To illustrate these potential gains, we propose practical
algorithms for constrained adaptive sensing by exploiting connections to the
theory of optimal experimental design and show that these algorithms exhibit
promising performance in some representative applications.

14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci