Ridge detection is a classical tool to extract curvilinear features in image processing. As such, it has great promise in applications to material science problems; specifically, for trend filtering relatively stable atom-shaped objects in image sequences, such as bright-field Transmission Electron Microscopy (TEM) videos. Standard analysis of TEM videos is limited to frame-by-frame object recognition. We instead harness temporal correlation across frames through simultaneous analysis of long image sequences, specified as a spatio-temporal image tensor. We define new ridge detection algorithms to non-parametrically estimate explicit trajectories of atomic-level object locations as a continuous function of time. Our approach is specially tailored to handle temporal analysis of objects that seemingly stochastically disappear and subsequently reappear throughout a sequence. We demonstrate that the proposed method is highly effective in simulation scenarios, and delivers notable performance improvements in TEM experiments compared to other material science benchmarks.

Unsupervised denoising is a crucial challenge in real-world imaging applications. Unsupervised deep-learning methods have demonstrated impressive performance on benchmarks based on synthetic noise. However, no metrics exist to evaluate these methods in an unsupervised fashion. This is highly problematic for the many practical applications where ground-truth clean images are not available. In this work, we propose two novel metrics: the unsupervised mean squared error (MSE) and the unsupervised peak signal-to-noise ratio (PSNR), which are computed using only noisy data. We provide a theoretical analysis of these metrics, showing that they are asymptotically consistent estimators of the supervised MSE and PSNR. Controlled numerical experiments with synthetic noise confirm that they provide accurate approximations in practice. We validate our approach on real-world data from two imaging modalities: videos in raw format and transmission electron microscopy. Our results demonstrate that the proposed metrics enable unsupervised evaluation of denoising methods based exclusively on noisy data.

Deep convolutional neural networks (CNNs) for video denoising are typically trained with supervision, assuming the availability of clean videos. However, in many applications, such as microscopy, noiseless videos are not available. To address this, we propose an Unsupervised Deep Video Denoiser (UDVD1), a CNN architecture designed to be trained exclusively with noisy data. The performance of UDVD is comparable to the supervised state-of-the-art, even when trained only on a single short noisy video. We demonstrate the promise of our approach in real-world imaging applications by denoising raw video, fluorescence-microscopy and electron-microscopy data. In contrast to many current approaches to video denoising, UDVD does not require explicit motion compensation. This is advantageous because motion compensation is computationally expensive, and can be unreliable when the input data are noisy. A gradient-based analysis reveals that UDVD automatically adapts to local motion in the input noisy videos. Thus, the network learns to perform implicit motion compensation, even though it is only trained for denoising.

Deep convolutional neural networks (CNNs) for image denoising are typically trained on large datasets. These models achieve the current state of the art, but they do not generalize well to data that deviate from the training distribution. Recent work has shown that it is possible to train denoisers on a single noisy image. These models adapt to the features of the test image, but their performance is limited by the small amount of information used to train them. Here we propose "GainTuning'', a methodology by which CNN models pre-trained on large datasets can be adaptively and selectively adjusted for individual test images. To avoid overfitting, GainTuning optimizes a single multiplicative scaling parameter (the “Gain”) of each channel in the convolutional layers of the CNN. We show that GainTuning improves state-of-the-art CNNs on standard image-denoising benchmarks, boosting their denoising performance on nearly every image in a held-out test set. These adaptive improvements are even more substantial for test images differing systematically from the training data, either in noise level or image type. We illustrate the potential of adaptive GainTuning in a scientific application to transmission-electron-microscope images, using a CNN that is pre-trained on synthetic data. In contrast to the existing methodology, GainTuning is able to faithfully reconstruct the structure of catalytic nanoparticles from these data at extremely low signal-to-noise ratios.