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In many applications, collecting truth images is a challenging and costly task, and the prerequisite of having a training dataset of truth images limits its applicability. This paper proposes a self-supervised deep learning method for solving inverse imaging problems that does not require any training samples. The proposed approach is built on a reparametrization of latent images using a convolutional neural network, and the reconstruction is motivated by approximating the minimum mean square error estimate of the latent image using a Langevin dynamics\u2013based Monte Carlo (MC) method. To efficiently sample the network weights in the context of image reconstruction, we propose a Langevin MC scheme called Adam-LD, inspired by the well-known optimizer in deep learning, Adam. The proposed method is applied to solve linear and nonlinear inverse problems, specifically, sparse-view computed tomography image reconstruction and phase retrieval. Our experiments demonstrate that the proposed method outperforms existing unsupervised or self-supervised solutions in terms of reconstruction quality.<\/jats:p>","DOI":"10.1137\/23m1548025","type":"journal-article","created":{"date-parts":[[2023,11,30]],"date-time":"2023-11-30T04:00:35Z","timestamp":1701316835000},"page":"2247-2284","source":"Crossref","is-referenced-by-count":9,"title":["Self-Supervised Deep Learning for Image Reconstruction: A Langevin Monte Carlo Approach"],"prefix":"10.1137","volume":"16","author":[{"given":"Ji","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics, National University of Singapore, Singapore. 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