Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gabor phase retrieval is severely ill-posed   The problem of reconstructing a function from the magnitudes of its frame
coefficients has recently been shown to be never uniformly stable in
infinite-dimensional spaces [5]. This result also holds for frames that are
possibly continuous [2]. On the other hand, the problem is always stable in
finite-dimensional settings. A prominent example of such a phase retrieval
problem is the recovery of a signal from the modulus of its Gabor transform. In
this paper, we study Gabor phase retrieval and ask how the stability degrades
on a natural family of finite-dimensional subspaces of the signal domain
$L^2(\mathbb{R})$. We prove that the stability constant scales at least
quadratically exponentially in the dimension of the subspaces. Our construction
also shows that typical priors such as sparsity or smoothness promoting
penalties do not constitute regularization terms for phase retrieval.

12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio