Nonlinear Compressive Sensing

There are subjects that are less covered than others. Mostly because it is less convenient to deal with them or maybe because they are islands of knowledge, i.e. a small set of people live in them untouched by the rest of the community because the waters have not receded yet (see What Island is Next ?). I made a request on LinkedIn for any references related to nonlinear compressive sensing without much explanation as to I meant by nonlinear. I look forward to more (just add them in the comment section) but here is what we have so far: 

• The whole field of 1bit Compressive Sensing and low quantization CS with their attendant solvers,
• Compressed Sensing with Nonlinear Observations by Thomas Blumensath (Sparsify solver)
• Some Algorithmic Problems and Results in Compressed Sensing by  Muthu Muthukrishnan 
• Poisson Compressed Sensing and Performance Bounds on Compressed Sensing with Poisson Noise by Rebecca Willett and Maxim Raginsky
• An Iteratively Reweighted Algorithm for Sparse Reconstruction of Subsurface Flow Properties from Nonlinear Dynamic Data by Lianlin Li and Jafarpour 
• Sparse Interactions: Identifying High-Dimensional Multilinear Systems via Compressed Sensing by  Nazer and Nowack 
• Using the Kernel Trick in Compressive Sensing: Accurate Signal Recovery from Fewer Measurements by  Qi and Hughes 
• Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation by Kekatos and Giannakis 
• Highly nonlinear approximations for sparse signals representations project: http://www.nonlinear-approx.info/overview/index.html
• Sundeep Rangan's generalized AMP algorithm supports arbitrary probabilistic output channels that, in effect, model output linearities such as quantization. (an implementation of GAMP is here) 
• Optimized measurements for kernel compressive sensing by  K. N. Ramamurthy and A. Spanias,
• Boolean solvers involved in Group Testing and Sudoku solving
• Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing by Yoav Shechtman, Yonina C. Eldar, Alexander Szameit, Mordechai Segev

Thanks to Matthieu Puigt, Phil Schniter and Karthikeyan Natesan Ramamurthy for responding to the query:


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