Image reconstruction from incomplete measurements is one basic task in imaging. While supervised deep learning has emerged as a powerful tool for image reconstruction in recent years, its applicability is limited by its prerequisite on a large number of latent images for model training. To extend the application of deep learning to the imaging tasks where acquisition of latent images is challenging, this article proposes an unsupervised deep learning method that trains a deep model for image reconstruction with the access limited to measurement data. We develop a Siamese network whose twin sub-networks perform reconstruction cooperatively on a pair of complementary spaces: the null space of the measurement matrix and the range space of its pseudo inverse. The Siamese network is trained by a self-supervised loss with three terms: a data consistency loss over available measurements in the range space, a data consistency loss between intermediate results in the null space, and a mutual consistency loss on the predictions of the twin sub-networks in the full space. The proposed method is applied to four imaging tasks from different applications, and extensive experiments have shown its advantages over existing unsupervised solutions.

Phase retrieval (PR) is a challenging nonlinear inverse problem in scientific imaging that involves reconstructing the phase of a signal from its intensity measurements. Recently, there has been an increasing interest in deep learning-based PR. Motivated by the challenge of collecting ground-truth (GT) images in many domains, this paper proposes a fully-unsupervised learning approach for PR, which trains an end-to-end deep model via a GT-free teacher-student online distillation framework. Specifically, a teacher model is trained using a self-expressive loss with noise resistance, while a student model is trained with a consistency loss on augmented data to exploit the teacher's dark knowledge. Additionally, we develop an enhanced unfolding network for both the teacher and student models. Extensive experiments show that our proposed approach outperforms existing unsupervised PR methods with higher computational efficiency and performs competitively against supervised methods.

Deep learning has become a prominent tool for video denoising. However, most existing deep video denoising methods require supervised training using noise-free videos. Collecting noise-free videos can be costly and challenging in many applications. Therefore, this paper aims to develop an unsupervised deep learning method for video denoising that only uses a single test noisy video for training. To achieve this, an unsupervised loss function is presented that provides an unbiased estimator of its supervised counterpart defined on noise-free video. Additionally, a temporal attention mechanism is proposed to exploit redundancy among frames. The experiments on video denoising demonstrate that the proposed unsupervised method outperforms existing unsupervised methods and remains competitive against recent supervised deep learning methods.

Compressive sampling (CS) is an efficient technique for imaging. This paper proposes a ground-truth (GT) free meta-learning method for CS, which leverages both ex-ternal and internal deep learning for unsupervised high-quality image reconstruction. The proposed method first trains a deep neural network (NN) via external meta-learning using only CS measurements, and then efficiently adapts the trained model to a test sample for exploiting sample-specific internal characteristic for performance gain. The meta-learning and model adaptation are built on an improved Stein's unbiased risk estimator (iSURE) that provides efficient computation and effective guidance for accurate prediction in the range space of the adjoint of the measurement matrix. To improve the learning and adaption on the null space of the measurement matrix, a modi-fied model-agnostic meta-learning scheme and a null-space consistency loss are proposed. In addition, a bias tuning scheme for unrolling NNs is introduced for further acceler-ation of model adaption. Experimental results have demonstrated that the proposed GT-free method performs well and can even compete with supervised methods.

Deep denoiser, the deep network for denoising, has been the focus of the recent development on image denoising. In the last few years, there is an increasing interest in developing unsupervised deep denoisers which only call unorganized noisy images without ground truth for training. Nevertheless, the performance of these unsupervised deep denoisers is not competitive to their supervised counterparts. Aiming at developing a more powerful unsupervised deep denoiser, this paper proposed a data augmentation technique, called recorrupted-to-recorrupted (R2R), to address the overfitting caused by the absence of truth images. For each noisy image, we showed that the cost function defined on the noisy/noisy image pairs constructed by the R2R method is statistically equivalent to its supervised counterpart defined on the noisy/truth image pairs. Extensive experiments showed that the proposed R2R method noticeably outperformed existing unsupervised deep denoisers, and is competitive to representative supervised deep denoisers.

In last few years, supervised deep learning has emerged as one powerful tool for image denoising, which trains a denoising network over an external dataset of noisy/clean image pairs. However, the requirement on a high-quality training dataset limits the broad applicability of the denoising networks. Recently, there have been a few works that allow training a denoising network on the set of external noisy images only. Taking one step further, this paper proposes a self-supervised learning method which only uses the input noisy image itself for training. In the proposed method, the network is trained with dropout on the pairs of Bernoulli-sampled instances of the input image, and the result is estimated by averaging the predictions generated from multiple instances of the trained model with dropout. The experiments show that the proposed method not only significantly outperforms existing single-image learning or non-learning methods, but also is competitive to the denoising networks trained on external datasets.