Compressive Sensing via Convolutional Factor Analysis

TL;DR

This paper introduces a convolutional factor analysis approach for compressive sensing that learns dictionaries from compressed data, enabling effective image reconstruction and recognition with limited measurements.

Contribution

It develops a novel ADMM-based algorithm for convolutional factor analysis in compressive sensing, incorporating deep multilayer models and stochastic unpooling for improved reconstruction and classification.

Findings

Achieves comparable classification accuracy with 30% measurements.

Upper layer dictionaries outperform bottom layers with very limited data.

Provides effective reconstruction with less than 10% measurements.

Abstract

We solve the compressive sensing problem via convolutional factor analysis, where the convolutional dictionaries are learned {\em in situ} from the compressed measurements. An alternating direction method of multipliers (ADMM) paradigm for compressive sensing inversion based on convolutional factor analysis is developed. The proposed algorithm provides reconstructed images as well as features, which can be directly used for recognition ($e.g.$, classification) tasks. When a deep (multilayer) model is constructed, a stochastic unpooling process is employed to build a generative model. During reconstruction and testing, we project the upper layer dictionary to the data level and only a single layer deconvolution is required. We demonstrate that using $\sim30\%$ (relative to pixel numbers) compressed measurements, the proposed model achieves the classification accuracy comparable to the original data on MNIST. We also observe that when the compressed measurements are very limited ($e.g.$, $<10\%$), the upper layer dictionary can provide better reconstruction results than the bottom layer.