Representation error reduction in compressive sensing using generative models with pivotal tuning

Reducing the transmitted data volume is essential for implementing networks with resource limited and energy-constrained devices. In this sense, compressive sensing becomes a powerful alternative as it moves the most computationally complex task to the central server node, in contrast to the traditional compression scheme. Recently a combination of compressive sensing and generative models has appeared, giving rise to Compressive Sensing using Generative Models (CSGM). Although CSGM reduce reconstruction errors, they introduce the so-called representation error. This paper proposes CSGM-Pivotal Tuning Inversion (CSGM-PTI), a technique based on model retraining in decompression time to reduce the representation error in CSGM. The idea of CSGM-PTI is to expand the scope of the generative model to include the desired signal. The results show robustness to noise and performance gains in signal reconstruction of up to 20% compared with Deep Image Prior (DIP), standalone CSGM, and Wavelet Thresholding (WT) techniques, all traditionally used in the related literature.