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Compressive sensing is a method to recover the original image fromundersampled measurements. In order to overcome the ill-posedness of thisinverse problem, image priors are used such as sparsity in the wavelet domain,minimum total-variation, or self-similarity. Recently, deep learning basedcompressive image recovery methods have been proposed and have yieldedstate-of-the-art performances. They used deep learning based data-drivenapproaches instead of hand-crafted image priors to solve the ill-posed inverseproblem with undersampled data. Ironically, training deep neural networks forthem requires "clean" ground truth images, but obtaining the best qualityimages from undersampled data requires well-trained deep neural networks. Toresolve this dilemma, we propose novel methods based on two well-groundedtheories: denoiser-approximate message passing and Stein's unbiased riskestimator. Our proposed methods were able to train deep learning based imagedenoisers from undersampled measurements without ground truth images andwithout image priors, and to recover images with state-of-the-art qualitiesfrom undersampled data. We evaluated our methods for various compressivesensing recovery problems with Gaussian random, coded diffraction pattern, andcompressive sensing MRI measurement matrices. Our methods yieldedstate-of-the-art performances for all cases without ground truth images andwithout image priors. They also yielded comparable performances to the methodswith ground truth data.

Training deep learning based image denoisers from undersampled measurements without ground truth and without image prior