Magnetic resonance imaging (MRI) is a noninvasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., computed tomography or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling; thus, there is a need for accurate, efficient reconstruction methods from undersampled data sets. In this article, we describe the use of plug-and-play (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then, we review several PnP methods for which the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from this perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.

The rapid development of 3D technology and computer vision applications has motivated a thrust of methodologies for depth acquisition and estimation. However, existing hardware and software acquisition methods have limited performance due to poor depth precision, low resolution, and high computational cost. In this paper, we present a computationally efficient method to estimate dense depth maps from sparse measurements. There are three main contributions. First, we provide empirical evidence that depth maps can be encoded much more sparsely than natural images using common dictionaries, such as wavelets and contourlets. We also show that a combined wavelet-contourlet dictionary achieves better performance than using either dictionary alone. Second, we propose an alternating direction method of multipliers (ADMM) for depth map reconstruction. A multiscale warm start procedure is proposed to speed up the convergence. Third, we propose a two-stage randomized sampling scheme to optimally choose the sampling locations, thus maximizing the reconstruction performance for a given sampling budget. Experimental results show that the proposed method produces high-quality dense depth estimates, and is robust to noisy measurements. Applications to real data in stereo matching are demonstrated.

Ground based long-range passive imaging systems often suffer from degraded image quality due to a turbulent atmosphere. While methods exist for removing such turbulent distortions, many are limited to static sequences which cannot be extended to dynamic scenes. In addition, the physics of the turbulence is often not integrated into the image reconstruction algorithm. In this paper, we present a unified method for atmospheric turbulence mitigation in both static and dynamic sequences. We are able to achieve better results compared to existing methods by utilizing (i) a novel space-time non-local averaging method to construct a reliable reference frame, (ii) a geometric consistency and a sharpness metric to generate the lucky frame, (iii) a physics-constrained prior model of the point spread function for blind deconvolution. Experimental results based on synthetic and real long-range turbulence sequences validate the performance of the proposed method.

Restoring images distorted by atmospheric turbulence is a ubiquitous problem in long-range imaging applications. While existing deep-learning-based methods have demonstrated promising results in specific testing conditions, they suffer from three limitations: (1) lack of generalization capability from synthetic training data to real turbulence data; (2) failure to scale, hence causing memory and speed challenges when extending the idea to a large number of frames; (3) lack of a fast and accurate simulator to generate data for training neural networks. In this paper, we introduce the turbulence mitigation transformer (TMT) that explicitly addresses these issues. TMT brings three contributions: Firstly, TMT explicitly uses turbulence physics by decoupling the turbulence degradation and introducing a multi-scale loss for removing distortion, thus improving effectiveness. Secondly, TMT presents a new attention module along the temporal axis to extract extra features efficiently, thus improving memory and speed. Thirdly, TMT introduces a new simulator based on the Fourier sampler, temporal correlation, and flexible kernel size, thus improving our capability to synthesize better training data. TMT outperforms state-of-the-art video restoration models, especially in generalizing from synthetic to real turbulence data.

We propose an adaptive learning procedure to learn patch-based image priors for image denoising. The new algorithm, called the expectation-maximization (EM) adaptation, takes a generic prior learned from a generic external database and adapts it to the noisy image to generate a specific prior. Different from existing methods that combine internal and external statistics in ad hoc ways, the proposed algorithm is rigorously derived from a Bayesian hyper-prior perspective. There are two contributions of this paper. First, we provide full derivation of the EM adaptation algorithm and demonstrate methods to improve the computational complexity. Second, in the absence of the latent clean image, we show how EM adaptation can be modified based on pre-filtering. The experimental results show that the proposed adaptation algorithm yields consistently better denoising results than the one without adaptation and is superior to several state-of-the-art algorithms.