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 "do log factors matter on optimal wavelet approximation and the foundations of compressed sensing"):
  Abstract: A signature result in compressed sensing is that Gaussian random sampling achieves stable and robust recovery of sparse vectors under optimal conditions on the number of measurements. However, in the context of image reconstruction, it has been extensively documented that sampling strategies based on Fourier measurements outperform this purportedly optimal approach. Motivated by this seeming paradox, we investigate the problem of optimal sampling for compressed sensing. Rigorously combining the theories of wavelet approximation and infinite-dimensional compressed sensing, our analysis leads to new error bounds in terms of the total number of measurements $m$ for the approximation of piecewise $\alpha$-Holder functions. In this setting, we show the suboptimality of random Gaussian sampling, exhibit a provably optimal sampling strategy and prove that Fourier sampling outperforms random Gaussian sampling when the Holder exponent $\alpha$ is large enough. This resolves the claimed paradox, and provides a clear theoretical justification for the practical success of compressed sensing techniques in imaging problems.

Includes members:
  Member "uniform recovery in infinite dimensional compressed sensing and applications to structured binary sampling":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the troublesome kernel why deep learning for inverse problems is typically unstable")
  Member "on oracle type local recovery guarantees in compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "close encounters of the binary kind signal reconstruction guarantees for compressive hadamard sampling with haar wavelet basis")
  Member "robustness to unknown error in sparse regularization":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the gap between theory and practice in function approximation with deep neural networks")
  Member "compressed sensing with local structure uniform recovery guarantees for the sparsity in levels class":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the troublesome kernel why deep learning for inverse problems is typically unstable")
  Member "compressed sensing with structured sparsity and structured acquisition":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "close encounters of the binary kind signal reconstruction guarantees for compressive hadamard sampling with haar wavelet basis")
  Member "structure dependent sampling in compressed sensing theoretical guarantees for tight frames":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in pde")
  Member "stable recovery of low dimensional cones in hilbert spaces one rip to rule them all":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the importance of phase in complex compressive sensing")
  Member "on the absence of the rip in real world applications of compressed sensing and the rip in levels":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "multilevel illumination coding for fourier transform interferometry in fluorescence spectroscopy")

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)