scholarly journals Geometric inference for general high-dimensional linear inverse problems

2016 ◽  
Vol 44 (4) ◽  
pp. 1536-1563 ◽  
Author(s):  
T. Tony Cai ◽  
Tengyuan Liang ◽  
Alexander Rakhlin
Keyword(s):  
Inverse Problems ◽  
High Dimensional ◽  
Linear Inverse Problems ◽  
Geometric Inference

scholarly journals Plug in estimation in high dimensional linear inverse problems a rigorous analysis

2019 ◽  
Vol 2019 (12) ◽  
pp. 124021 ◽  
Author(s):  
Alyson K Fletcher ◽  
Parthe Pandit ◽  
Sundeep Rangan ◽  
Subrata Sarkar ◽  
Philip Schniter
Keyword(s):  
Inverse Problems ◽  
High Dimensional ◽  
Rigorous Analysis ◽  
Linear Inverse Problems

scholarly journals Fundamental Performance Limits for Ideal Decoders in High-Dimensional Linear Inverse Problems

2014 ◽  
Vol 60 (12) ◽  
pp. 7928-7946 ◽  
Author(s):  
Anthony Bourrier ◽  
Mike E. Davies ◽  
Tomer Peleg ◽  
Patrick Perez ◽  
Remi Gribonval
Keyword(s):  
Inverse Problems ◽  
High Dimensional ◽  
Performance Limits ◽  
Linear Inverse Problems

scholarly journals AMP-Inspired Deep Networks for Sparse Linear Inverse Problems

2017 ◽  
Vol 65 (16) ◽  
pp. 4293-4308 ◽  
Author(s):  
Mark Borgerding ◽  
Philip Schniter ◽  
Sundeep Rangan
Keyword(s):  
Inverse Problems ◽  
Linear Inverse Problems ◽  
Deep Networks

scholarly journals The Regularized Weak Functional Matching Pursuit for linear inverse problems

2019 ◽  
Vol 27 (3) ◽  
pp. 317-340 ◽  
Author(s):  
Max Kontak ◽  
Volker Michel
Keyword(s):  
Inverse Problems ◽  
Matching Pursuit ◽  
A Priori ◽  
Computation Time ◽  
Point Of View ◽  
Computational Point ◽  
Linear Inverse Problems ◽  
Infinite Dimensional ◽  
Frame Condition ◽  
Ill Posed

Abstract In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the “weak” approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90  of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.

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