human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "nonlinear frames and sparse reconstructions in banach spaces"):
  Abstract: In the first part of this paper, we consider nonlinear extension of frame theory by introducing bi-Lipschitz maps $F$ between Banach spaces. Our linear model of bi-Lipschitz maps is the analysis operator associated with Hilbert frames, $p$-frames, Banach frames, g-frames and fusion frames. In general Banach space setting, stable algorithm to reconstruct a signal $x$ from its noisy measurement $F(x)+\epsilon$ may not exist. In this paper, we establish exponential convergence of two iterative reconstruction algorithms when $F$ is not too far from some bounded below linear operator with bounded pseudo-inverse, and when $F$ is a well-localized map between two Banach spaces with dense Hilbert subspaces. The crucial step to prove the later conclusion is a novel fixed point theorem for a well-localized map on a Banach space. #R##N#In the second part of this paper, we consider stable reconstruction of sparse signals in a union ${\bf A}$ of closed linear subspaces of a Hilbert space ${\bf H}$ from their nonlinear measurements. We create an optimization framework called sparse approximation triple $({\bf A}, {\bf M}, {\bf H})$, and show that the minimizer $$x^*={\rm argmin}_{\hat x\in {\mathbf M}\ {\rm with} \ \|F(\hat x)-F(x^0)\|\le \epsilon} \|\hat x\|_{\mathbf M}$$ provides a suboptimal approximation to the original sparse signal $x^0\in {\bf A}$ when the measurement map $F$ has the sparse Riesz property and almost linear property on ${\mathbf A}$. The above two new properties is also discussed in this paper when $F$ is not far away from a linear measurement operator $T$ having the restricted isometry property.

Includes members:
  Member "does ell_p minimization outperform ell_1 minimization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "optimal data detection in large mimo")
  Member "spatially distributed sampling and reconstruction":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "stable phaseless sampling and reconstruction of real valued signals with finite rate of innovations")
  Member "sampling and galerkin reconstruction in reproducing kernel spaces":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "spatially distributed sampling and reconstruction")
  Member "sharp rip bound for sparse signal and low rank matrix recovery":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a deterministic convergence framework for exact non convex phase retrieval")
  Member "phase retrieval stability and recovery guarantees":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "consensus based optimization on the sphere ii convergence to global minimizers and machine learning")
  Member "sparsity constrained nonlinear optimization optimality conditions and algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "efficient relaxed gradient support pursuit for sparsity constrained non convex optimization")
  Member "phaselift exact and stable signal recovery from magnitude measurements via convex programming":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "deep s 3 pr simultaneous source separation and phase retrieval using deep generative models")
  Member "sparse approximation property and stable recovery of sparse signals from noisy measurements":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "matrix recovery from rank one projection measurements via nonconvex minimization")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.IT(Information Theory)