Machine learning for signal processing

Data-driven frequency estimation

Frequency 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.

Learning-based denoising

We show that deep convolutional neural networks can be rendered robust to changes in noise level by removing additive terms in the architecture. Locally, the networks act linearly on the noisy image, enabling direct analysis of their behavior via linear-algebraic tools. These analyses provide interpretations of network functionality in terms of nonlinear adaptive filtering, and projection onto a union of low-dimensional subspaces, connecting the learning-based method to more traditional denoising methodology.

Theory of inverse problems

Separable nonlinear inverse problems

Compressed-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 deconvolution

Estimation 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 sources

We 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.

Data science for healthcare

Quantitative rehabilitation of stroke patients

In 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 fingerprinting

Magnetic 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 learning

We design 3D convolutional neural network to detect Alzheimer's Disease using structural brain MRI scans.

Analysis of infant-sleep patterns

We 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 sensing

Undersampling 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).