# Deep learned SVT: Unrolling singular value thresholding to obtain better MSE

arXiv: https://arxiv.org/abs/2105.06934 · HTML: https://mlsanity.com/paper/2105.06934/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 14 May 2021.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound](https://mlsanity.com/paper/1811.08252/) (2018)
- [A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements](https://mlsanity.com/paper/1506.06081/) (2015)

## Built on by (most cited first, 1 of 1)

- [SATORIS-N: Spectral Analysis based Traffic Observation Recovery via Informed Subspaces and Nuclear-norm minimization](https://mlsanity.com/paper/2602.03138/) (2026)

## Abstract (arXiv)

Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a trainable deep neural network by unrolling a popular iterative algorithm called the singular value thresholding (SVT) algorithm to perform this generalized matrix completion which we call Learned SVT (LSVT). We show that our proposed LSVT with fixed layers (say T) reconstructs the matrix with lesser mean squared error (MSE) compared with that incurred by SVT with fixed (same T) number of iterations and our method is much more robust to the parameters which need to be carefully chosen in SVT algorithm.