ProjectsMachine LearningEarly learning and memorizationWe analyze the phenomena of early learning and memorization in deep neural networks and exploit to design methodology for probability estimation, and classification and segmentation from noisy labels.
Learning-based denoisingMotivated by applications in scientific imaging, and specifically in electron microscopy, we have analyzed the robustness of deep neural networks trained for denoising and developed methodology for unsupervised and semi-supervised denoising.
Data-driven frequency estimationFrequency estimation is a fundamental problem in signal processing, with applications in radar imaging, underwater acoustics, seismic imaging, and spectroscopy. The goal is to estimate the frequency of each component in a multisinusoidal signal from a finite number of noisy samples. We propose a learning-based framework for frequency estimation that achieves state-of-the-art results.
Data Science in MedicineQuantitative rehabilitation of stroke patientsIn collaboration with the Mobilis lab at the NYU School of Medicine we are designing deep-learning methodology to perform automatic identification and counting of functional arm movements in stroke patients from measurements obtained with wearable sensors.
Magnetic resonance fingerprintingMagnetic resonance fingerprinting (MRF) is a recently-developed technique for quantitative estimation of tissue parameters in the human body. These parameters have great potential as biomarkers for various pathologies, and allow to synthesize images with standardized contrasts. Our work focuses on (1) optimizing measurement design, and (2) adapting the MRF framework to account for the presence of several tissues in each voxel.
Automatic diagnostics via deep learningWe design 3D convolutional neural network to detect Alzheimer's Disease using structural brain MRI scans.
Analysis of infant-sleep patternsWe propose a nonparametric model for time series with missing data based on regularized nonnegative low-rank matrix factorization. The model expresses each instance in a set of time series as a linear combination of a small number of shared basis functions. The methodology is applied to a large real-world dataset of infant-sleep data gathered by caregivers with a mobile-phone app.
Parallel magnetic-resonance imaging and compressed sensingUndersampling images in the frequency domain enables accelerated acquisition in magnetic resonance imaging. Here we study how to combine two complementary approaches: parallel imaging (i.e. using multiple coils with different sensitivities to gather the data), and compressed sensing (i.e. randomizing the sampling pattern, and exploiting image sparsity in a transform domain).
Theory of Inverse ProblemsSeparable nonlinear inverse problemsCompressed-sensing theory does not explain the success of convex-programming methods for deterministic inverse problems where the measurement operator is highly locally coherent. Examples include spike deconvolution, heat-source localization and estimation of brain activity from electroencephalography data. We build a general theory of sparse recovery adapted to such settings.
Sampling theorems for deconvolutionEstimation of spikes from samples of their convolution with a smooth kernel is an important inverse problem in imaging and reflection seismography. Here we establish a sampling theorem, showing that exact and robust recovery via convex programming is possible from any sampling pattern that contains two samples close to each spike, as long as the signal satisfies a minimum-separation condition.
Super-resolution of point sourcesWe consider the problem of super-resolving point sources from low-pass data via convex programming and the related problem of super-resolving the spectrum of a multisinusoidal signal from a finite number of samples. We establish exact-recovery and stability guarantees under a minimum separation condition, as well as robustness to outliers.
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