Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees. However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix leads to reconstruction problems that are intractable or non-convex optimizations. Past work has dealt …
This talk will follow up on last week’s SILO talk by Prof. Ellenberg. In particular, this will be a discussion about the “EDSN” algorithm for robust and efficient hierarchical clustering. Hierarchical clustering based on pairwise similarities is a common tool used in a broad range of scientific applications. However, in …
This talk introduces a way to conduct audio morphings by imposing a constraint that can be used to smoothly connect two different audio spectra. The method exploits a formal analogy between the two spatial dimensions of Laplace’s partial differential equation and the two dimensions (time and frequency) of a spectrogram. …
We study the generation of secret keys based on the inherent randomness of wireless multipath channels. This study falls into the broad area of physical layer security. In this setting the objective is for a pair of users, Alice and Bob, to extract a secret key from a natually occurring …
Statistical testing is a ubiquitous in engineering and science. The outcomes of testing and the significance we attach to them have profound effects on society; e.g., they are the basis for many public health and other social-engineering initiatives. So, it is crucial that we all agree and understand what it …
Low-dimensional linear subspace approximations to high-dimensional data are a common approach to handling problems of estimation, detection and prediction, with applications such as network monitoring, collaborative filtering, object tracking in computer vision, and environmental sensing. Corrupt and missing data are the norm in many high-dimensional situations, not only because of …
When I was a naive undergraduate and disenchanted with the prospect of becoming a math professor, I enrolled in graduate school at MIT to work on computer music. My career as an electroacoustic scholar ended quickly but opened my eyes to the world of interactive sound art. In this talk, …
Identification of the nature of interactions between different cortical regions is an important step towards better understanding of healthy and diseased brain function. Electroencephalography (EEG) and magnetoencephalography (MEG) offer a window on the electrical behavior of cortical neuronal populations through non-invasive measurement of the electric and magnetic fields, respectively, they …
The fact that sparse vectors can be recovered from a small number of linear measurements has important and exciting implications for engineering and statistics. However, despite the vast amount of recent work in the field of compressed sensing, a sharp characterization between what can and cannot be recovered in the …
A self-contained lecture on the Discrete Fourier Transform and its relation to the time and frequency representations of a signal. By describing time-shift and frequency-shift operators with a structure known as the Heisenberg group, explicit steps can be given for producing an FFT algorithm. Pseudocode and programmable examples will be …