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 Paper ID IVMSP-30.1 Paper Title NON-CONVEX SPARSE DEVIATION MODELING VIA GENERATIVE MODELS Authors Yaxi Yang, Hailin Wang, Southwest University, China; Haiquan Qiu, Xi’an Jiaotong University, China; Jianjun Wang, Southwest University, China; Yao Wang, Xi’an Jiaotong University, China Session IVMSP-30: Inverse Problems in Image & Video Processing Location Gather.Town Session Time: Friday, 11 June, 13:00 - 13:45 Presentation Time: Friday, 11 June, 13:00 - 13:45 Presentation Poster Topic Image, Video, and Multidimensional Signal Processing: [IVTEC] Image & Video Processing Techniques IEEE Xplore Open Preview Click here to view in IEEE Xplore Virtual Presentation Click here to watch in the Virtual Conference Abstract In this paper, the generative model is used to introduce the structural properties of the signal to replace the common sparse hypothesis, and a non-convex compressed sensing sparse deviation model based on the generative model ($\ell_q$-Gen) is proposed. By establishing $\ell_q$ variant of the restricted isometry property ($q$-RIP) and Set-Restricted Eigenvalue Condition ($q$-$S$-REC), the error upper bound of the optimal decoder is derived when the recovered signal is within the sparse deviation range of the generator. Furthermore, it is proved that the Gaussian matrix satisfying a certain number of measurements is sufficient to ensure a good recovery for the generating function with high probability. Finally, a series of experiments are carried out to verify the effectiveness and superiority of the $\ell_q$-Gen model.