The long overview paper, Multidimensional Filter Banks and Multiscale Geometric Representations, provides a systematic development of the theory and constructions of multidimensional filter banks and sparse representations that can efficiently capture directional and geometric features of multidimensional signals.

The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In the paper A Spectral Graph Uncertainty Principle, we investigate a spectral graph analogy to Heisenberg's celebrated uncertainty principle.

A. Agaskar and Y. M. Lu, Uncertainty principles for signals defined on graphs: Bounds and characterizations.

Y. Xiong and Y. M. Lu, Blind estimation and low-rate sampling of sparse MIMO systems with common support.

Before the advent of digital image sensors, photography, for the most part of its history, used film to record light information. In the paper Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics, we study a new digital image sensor that is reminiscent of photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity.

The paper Can One Hear the Shape of a Room: The 2-D Polygonal Case was awarded the Best Student Paper Award at the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) in 2011. In a famous work, M. Kac asks the catchy question “Can you hear the shape of a drum?”. This problem is related to a question in astrophysics, and the answer is negative, meaning, different drum shapes can have the same resonant frequencies.