Title:  Sketching For Imaging And Inference In High Dimensions

Committee: 

Dr. Romberg, Advisor    

Dr. Davenport, Chair

Dr. Koltchinskii

Dr. Lee

Abstract:

The objective of the proposed research is to study the application of dimensionality reduction techniques, particularly the sketching paradigm to fundamental machine learning and signal processing algorithms such as linear regression, ridge regression, low rank matrix recovery and phase retrieval. The emphasis is on (i) considering practical and physical constraints on the sketching system, particularly in systems such as sensor arrays and in applications involving decentralized data acquisition (ii) on rigorous theoretical analysis of such systems. The proposed work targets four specific aims: (i)To study a trade-off between excitation bandwidth and the number of spatial array measurements required for far-field range-limited target imaging and to analyze block diagonal sketching matrices in the context of ridge regression (ii) To design and analyze fast algorithms for broadband DOA estimation from highly subsampled array data (iii) To model and study the problem of low rank matrix recovery in a decentralized data acquisition scenario (iv) To analyze the low rank phase retrieval problem and design an algorithm for joint signal recovery of samples from a subspace.