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Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…

Medical Informatics and the application of modern signal processing in the assistance of the diagnostic process in medical imaging is one of the more recent and active research areas today. This thesis addresses a variety of issues related…

Medical image enhancement is crucial for improving the quality and interpretability of diagnostic images, ultimately supporting early detection, accurate diagnosis, and effective treatment planning. Despite advancements in imaging…

In the 70s a novel branch of statistics emerged focusing its effort in selecting a function in the pattern recognition problem, which fulfils a definite relationship between the quality of the approximation and its complexity. These…

Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…

Due to the complexity of medical image acquisition and the difficulty of annotation, medical image datasets inevitably contain noise. Noisy data with wrong labels affects the robustness and generalization ability of deep neural networks.…

Condensed phase systems often exhibit a mixture of deterministic and stochastic dynamics at the nanoscale which are essential to understanding their function, but can be challenging to study directly using conventional imaging methods.…

Anomaly detection in medical images refers to the identification of abnormal images with only normal images in the training set. Most existing methods solve this problem with a self-reconstruction framework, which tends to learn an identity…

In safety-critical applications like medical diagnosis, certainty associated with a model's prediction is just as important as its accuracy. Consequently, uncertainty estimation and reduction play a crucial role. Uncertainty in predictions…

The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate…

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

Artifacts pose a significant challenge in medical imaging, impacting diagnostic accuracy and downstream analysis. While image-based approaches for detecting artifacts can be effective, they often rely on preprocessing methods that can lead…

Image-to-image regression is an important learning task, used frequently in biological imaging. Current algorithms, however, do not generally offer statistical guarantees that protect against a model's mistakes and hallucinations. To…

Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…

Magnetic resonance imaging (MRI) is an essential medical tool with inherently slow data acquisition process. Slow acquisition process requires patient to be long time exposed to scanning apparatus. In recent years significant efforts are…

This work focuses on assessing the information-theoretic limits of scene parameter estimation in plenoptic imaging systems. A general framework to compute lower bounds on the parameter estimation error from noisy plenoptic observations is…

In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…

Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…

For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the…