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 "ell 1 analysis minimization and generalized co sparsity when does recovery succeed"):
  Abstract: This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the $\ell^{1}$-analysis basis pursuit, enabling highly accurate predictions of its sample complexity. The corresponding bounds on the number of required measurements do explicitly depend on the Gram matrix of the analysis operator and therefore particularly account for its mutual coherence structure. Our findings defy conventional wisdom which promotes the sparsity of analysis coefficients as the crucial quantity to study. In fact, this common paradigm breaks down completely in many situations of practical interest, for instance, when applying a redundant (multilevel) frame as analysis prior. By extensive numerical experiments, we demonstrate that, in contrast, our theoretical sampling-rate bounds reliably capture the recovery capability of various examples, such as redundant Haar wavelets systems, total variation, or random frames. The proofs of our main results build upon recent achievements in the convex geometry of data mining problems. More precisely, we establish a sophisticated upper bound on the conic Gaussian mean width that is associated with the underlying $\ell^{1}$-analysis polytope. Due to a novel localization argument, it turns out that the presented framework naturally extends to stable recovery, allowing us to incorporate compressible coefficient sequences as well.

Includes members:
  Member "learning co sparse analysis operators with separable structures":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "convolutional analysis operator learning dependence on training data")
  Member "precise phase transition of total variation minimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "compressive sensing with redundant dictionaries and structured measurements":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "sub gaussian matrices on sets optimal tail dependence and applications")
  Member "robust analysis l1 recovery from gaussian measurements and total variation minimization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "structure dependent sampling in compressed sensing theoretical guarantees for tight frames":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "do log factors matter on optimal wavelet approximation and the foundations of compressed sensing")
  Member "on the effective measure of dimension in the analysis cosparse model":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "living near the edge a lower bound on the phase transition of total variation minimization")
  Member "projection onto the cosparse set is np hard":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "quantized compressive sensing with rip matrices the benefit of dithering")
  Member "analysis operator learning and its application to image reconstruction":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "controlling neural networks via energy dissipation")

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)