Simultaneous compressive image recovery and deep denoiser learning from undersampled measurements

Compressive image recovery utilizes sparse image priors such as wavelet l1 norm, total-variation (TV) norm, or self-similarity to reconstruct good quality images from highly compressive samples. Recently, there have been some attempts to exploit data-driven image priors from massive amount of clean images in compressive image recovery such as LDAMP algorithm. By utilizing large-scale noiseless images for training deep neural network denoisers, LDAMP outperformed other conventional compressive image reconstruction methods. However, one drawback of LDAMP is that large-scale noiseless images must be acquired for deep learning based denoisers. In this article, we propose a method for simultaneous compressive image recovery and deep denoiser learning from undersampled measurements that enables compressive image recovery methods to use data-driven image priors when only large-scale compressive samples are available without ground truth images. By utilizing the structure of LDAMP and Stein's Unbiased Risk Estimator (SURE) based deep neural network denoiser, we showed that our proposed methods were able to achieve better performance than other methods such as conventional BM3D-AMP and LDAMP methods trained with the results of BM3D-AMP for training data and/or testing data for all cases with i.i.d. Gaussian random and coded diffraction measurement matrices at various compression ratios. We also investigated accurate noise level estimation methods in LDAMP for coded diffraction measurement matrix to train deep denoiser networks for high performance.