Diffusion models demonstrate state-of-the-art performance on image generation, and are gaining traction for sparse medical image reconstruction tasks. However, compared to classical reconstruction algorithms relying on simple analytical priors, diffusion models have the dangerous property of producing realistic looking results \emph{even when incorrect}, particularly with few observations. We investigate the utility of diffusion models as priors for image reconstruction by varying the number of observations and comparing their performance to classical priors (sparse and Tikhonov regularization) using pixel-based, structural, and downstream metrics. We make comparisons on low-dose chest wall computed tomography (CT) for fat mass quantification. First, we find that classical priors are superior to diffusion priors when the number of projections is ``sufficient''. Second, we find that diffusion priors can capture a large amount of detail with very few observations, significantly outperforming classical priors. However, they fall short of capturing all details, even with many observations. Finally, we find that the performance of diffusion priors plateau after extremely few ($\approx$10-15) projections. Ultimately, our work highlights potential issues with diffusion-based sparse reconstruction and underscores the importance of further investigation, particularly in high-stakes clinical settings.

Implicit neural representations (INRs) have demonstrated success in a variety of applications, including inverse problems and neural rendering. An INR is typically trained to capture one signal of interest, resulting in learned neural features that are highly attuned to that signal. Assumed to be less generalizable, we explore the aspect of transferability of such learned neural features for fitting similar signals. We introduce a new INR training framework, STRAINER that learns transferrable features for fitting INRs to new signals from a given distribution, faster and with better reconstruction quality. Owing to the sequential layer-wise affine operations in an INR, we propose to learn transferable representations by sharing initial encoder layers across multiple INRs with independent decoder layers. At test time, the learned encoder representations are transferred as initialization for an otherwise randomly initialized INR. We find STRAINER to yield extremely powerful initialization for fitting images from the same domain and allow for $\approx +10dB$ gain in signal quality early on compared to an untrained INR itself. STRAINER also provides a simple way to encode data-driven priors in INRs. We evaluate STRAINER on multiple in-domain and out-of-domain signal fitting tasks and inverse problems and further provide detailed analysis and discussion on the transferability of STRAINER's features. Our demo can be accessed at https://kushalvyas.github.io/strainer.html .

Uncertainty quantification is crucial to account for the imperfect predictions of machine learning algorithms for high-impact applications. Conformal prediction (CP) is a powerful framework for uncertainty quantification that generates calibrated prediction intervals with valid coverage. In this work, we study how CP intervals are affected by bias - the systematic deviation of a prediction from ground truth values - a phenomenon prevalent in many real-world applications. We investigate the influence of bias on interval lengths of two different types of adjustments -- symmetric adjustments, the conventional method where both sides of the interval are adjusted equally, and asymmetric adjustments, a more flexible method where the interval can be adjusted unequally in positive or negative directions. We present theoretical and empirical analyses characterizing how symmetric and asymmetric adjustments impact the "tightness" of CP intervals for regression tasks. Specifically for absolute residual and quantile-based non-conformity scores, we prove: 1) the upper bound of symmetrically adjusted interval lengths increases by $2|b|$ where $b$ is a globally applied scalar value representing bias, 2) asymmetrically adjusted interval lengths are not affected by bias, and 3) conditions when asymmetrically adjusted interval lengths are guaranteed to be smaller than symmetric ones. Our analyses suggest that even if predictions exhibit significant drift from ground truth values, asymmetrically adjusted intervals are still able to maintain the same tightness and validity of intervals as if the drift had never happened, while symmetric ones significantly inflate the lengths. We demonstrate our theoretical results with two real-world prediction tasks: sparse-view computed tomography (CT) reconstruction and time-series weather forecasting. Our work paves the way for more bias-robust machine learning systems.

Understanding local risks from extreme rainfall, such as flooding, requires both long records (to sample rare events) and high-resolution products (to assess localized hazards). Unfortunately, there is a dearth of long-record and high-resolution products that can be used to understand local risk and precipitation science. In this paper, we present a novel generative diffusion model that downscales (super-resolves) globally available Climate Prediction Center (CPC) gauge-based precipitation products and ERA5 reanalysis data to generate kilometer-scale precipitation estimates. Downscaling gauge-based precipitation from 55 km to 1 km while recovering extreme rainfall signals poses significant challenges. To enforce our model (named WassDiff) to produce well-calibrated precipitation intensity values, we introduce a Wasserstein Distance Regularization (WDR) term for the score-matching training objective in the diffusion denoising process. We show that WDR greatly enhances the model's ability to capture extreme values compared to diffusion without WDR. Extensive evaluation shows that WassDiff has better reconstruction accuracy and bias scores than conventional score-based diffusion models. Case studies of extreme weather phenomena, like tropical storms and cold fronts, demonstrate WassDiff's ability to produce appropriate spatial patterns while capturing extremes. Such downscaling capability enables the generation of extensive km-scale precipitation datasets from existing historical global gauge records and current gauge measurements in areas without high-resolution radar.

Reflections on glossy objects contain valuable and hidden information about the surrounding environment. By converting these objects into cameras, we can unlock exciting applications, including imaging beyond the camera's field-of-view and from seemingly impossible vantage points, e.g. from reflections on the human eye. However, this task is challenging because reflections depend jointly on object geometry, material properties, the 3D environment, and the observer viewing direction. Our approach converts glossy objects with unknown geometry into radiance-field cameras to image the world from the object's perspective. Our key insight is to convert the object surface into a virtual sensor that captures cast reflections as a 2D projection of the 5D environment radiance field visible to the object. We show that recovering the environment radiance fields enables depth and radiance estimation from the object to its surroundings in addition to beyond field-of-view novel-view synthesis, i.e. rendering of novel views that are only directly-visible to the glossy object present in the scene, but not the observer. Moreover, using the radiance field we can image around occluders caused by close-by objects in the scene. Our method is trained end-to-end on multi-view images of the object and jointly estimates object geometry, diffuse radiance, and the 5D environment radiance field.

The current trend of pushing CNNs deeper with convolutions has created a pressing demand to achieve higher compression gains on CNNs where convolutions dominate the computation and parameter amount (e.g., GoogLeNet, ResNet and Wide ResNet). Further, the high energy consumption of convolutions limits its deployment on mobile devices. To this end, we proposed a simple yet effective scheme for compressing convolutions though applying k-means clustering on the weights, compression is achieved through weight-sharing, by only recording $K$ cluster centers and weight assignment indexes. We then introduced a novel spectrally relaxed $k$-means regularization, which tends to make hard assignments of convolutional layer weights to $K$ learned cluster centers during re-training. We additionally propose an improved set of metrics to estimate energy consumption of CNN hardware implementations, whose estimation results are verified to be consistent with previously proposed energy estimation tool extrapolated from actual hardware measurements. We finally evaluated Deep $k$-Means across several CNN models in terms of both compression ratio and energy consumption reduction, observing promising results without incurring accuracy loss. The code is available at https://github.com/Sandbox3aster/Deep-K-Means

Phase retrieval (PR) algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging PR algorithms enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional PR algorithms struggle in the presence of noise. Recently PR algorithms have been developed that use priors to make themselves more robust. However, these algorithms often require unrealistic (Gaussian or coded diffraction pattern) measurement models and offer slow computation times. These drawbacks have hindered widespread adoption. In this work we use convolutional neural networks, a powerful tool from machine learning, to regularize phase retrieval problems and improve recovery performance. We test our new algorithm, prDeep, in simulation and demonstrate that it is robust to noise, can handle a variety system models, and operates fast enough for high-resolution applications.