# Tradeoffs between Convergence Speed and Reconstruction Accuracy in Inverse Problems

Accepted

Journal Article

IEEE Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially limiting the achievable accuracy. Given an error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain faster convergence to a minimizer achieving the allowed error without increasing the computational cost of each iteration considerably. Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set may lead to a faster convergence at the cost of an additional error in the reconstruction related to the accuracy of the set approximation. Our theory ties to recent advances in sparse recovery, compressed sensing, and deep learning. Particularly, it may provide a possible explanation to the successful approximation of the l_1-minimization solution by neural networks with layers representing iterations, as practiced in the learned iterative shrinkage-thresholding algorithm (LISTA).

### Full Text

### Duke Authors

### Cited Authors

- Giryes, R; Eldar, YC; Bronstein, A; Sapiro, G

### Published Date

- January 10, 2018

### Published In

### International Standard Serial Number (ISSN)

- 1053-587X

### Digital Object Identifier (DOI)

- 10.1109/TSP.2018.2791945

### Citation Source

- Scopus