# Dictionary Learning for Blind One Bit Compressed Sensing

arXiv: https://arxiv.org/abs/1508.07648 · HTML: https://mlsanity.com/paper/1508.07648/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2015.

## Built on by (most cited first, 5 of 5)

- [Learning to Reconstruct Signals From Binary Measurements](https://mlsanity.com/paper/2303.08691/) (2023)
- [DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds](https://mlsanity.com/paper/2205.07050/) (2022)
- [Generalization analysis of an unfolding network for analysis-based Compressed Sensing](https://mlsanity.com/paper/2303.05582/) (2023)
- [One-Bit Compressive Sensing: Can We Go Deep and Blind?](https://mlsanity.com/paper/2203.11278/) (2022)
- [Convex Quantization Preserves Logconcavity](https://mlsanity.com/paper/2206.05598/) (2022)

## Abstract (arXiv)

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix Ab and sparse domain matrix Phi, ie Db=AbPhi, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix Db. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements.