Statistical Signal Processing

Posted By admin On 23/08/21

Statistical signal processing has its roots in probability theory, mathematical statistics and, more recently, systems theory and statistical communications theory. A Wavelet Tour of Signal Processing (Mallat), Pattern Recognition and Machine Learning (Bishop), A Probabilistic Theory of Pattern Recognition (Devroye, Gyorfi, and Lugosi), Elements of Statistical Learning (Hastie, Tibshirani, and Friedman). Google maps: just awesome.

Class Schedule for Spring 2020

WeekTopicHW (Due Thursdays)
1
1/13
Class organization.
Probability: random variables and random vectors, expected values, characteristic functions.
Random processes: Definitions
Tuesday, Thursday
2
1/20
Random processes: Second-order description (mean, correlation function, power spectrum).
Linear vector spaces: inner products, norms, Hilbert spaces, separability.
Tuesday, Thursday
PS I: 2.3, 2.4, 2.8, 2.10, 2.11
3
1/27
Vector space for random processes: inner product, Karhunen-Loève expansion.
Optimization theory: constrained and unconstrained problems.
Estimation theory: notions of error.
Tuesday, Thursday
PS II: 2.17, 2.19, 2.35, 2.47
4
2/3
Estimation theory: parameter estimation, minimum mean-squared error estimation, MAP estimation, linear estimators and the Orthogonality Principle, maximum likelihood estimation, Cramér-Rao bound.
Tuesday, Tuesday audio backup, Thursday
PS III: 2.14, 2.16, 3.1, 4.1
5
2/10
Estimation theory: The Cramér-Rao bound.
Poisson processes and estimating their characteristics.
Tuesday, Thursday
Spring Recess
6
2/17
Linear and nonlinear waveform parameter estimates. Linear signal estimation: Wiener filters.
Tuesday, Thursday
PS IV: 4.2, 4.3, 4.9, 4.11, 4.14
7
2/24
Linear signal estimation: Wiener filters, adaptive filters.
Tuesday, Thursday
PS V: 4.8, 4.12, 4.16, 4.23
8
3/2
Linear signal estimation: Kalman filters. General signal estimation: Bayesian filtering.
Tuesday (missing some audio), (backup audio); Thursday
Quiz I Due
9
3/9
Estimation theory: spectral estimation.
Filtering in the context of basis expansions: Denoising, wavelets, compressive sensing.
Detection theory: likelihood ratio test.
Tuesday, Thursday
10
3/16
Spring Break
11
3/23
Detection theory: ROC curves, Neymann-Pearson detection, Stein’s lemma.
Tuesday, Thursday
PS VI: 4.31, 4.36, 4.38, 4.41
12
3/30
Distance measures for densities, M models, null-hypothesis testing.
Tuesday
PS VII: 4.44, 4.46, 4.54, 5.1
13
4/6
Sequential detection.
Uncertainties in models: simultaneous estimation and detection.
Tuesday, Thursday
PS VIII: 5.2, 5.4, 5.6, 5.10, 5.13
14
4/13
Detection theory: Signals in additive noise.
Signal and noise unknowns.
Tuesday, Thursday
PS IX: 5.5, 5.23, 5.27, 5.51
15
4/20
Non-Gaussian detection theory, type-based detection.
Tuesday, Thursday
Quiz II Due
Professor, Electrical & Computer Engineering, Cornell.
Vikram is also affiliated with Center of Applied Math and Mechanical & Aerospace Engineering at Cornell.
Vikram is a Fellow of IEEE, served as distinguished lecturer for the IEEE Signal Processing Society, Editor in Chief of IEEE Journal Selected Topics in Signal Processing. He was awarded an honorary doctorate from KTH, Sweden in 2013.
Vikram’s research interests are in statistical signal processing, stochastic control (POMDPs), stochastic optimization and inverse reinforcement learning with applications in social networks, human decision making and adaptive sensing.
  • Click here for all my publications.
  • Click here for preprints on arXiv
  • Recent papers: JMLR,IEEE Info Theory, ICML, Nature Comm, IEEE Automatic Control, IEEE Signal Proc (Inverse RL for Identifying Cognitive Radar), IEEE Signal Proc (Inverse HMM Filters and Counter-adversarial Systems), IEEE Signal Proc (Anticipatory Decision Making and Quickest Change Detection).
Fundamental AreasApplication Areas
POMDPs & Controlled SensingSocial Networks (fusion & control)
Stochastic Optimization, Game TheoryCognitive Radar & Intent Inference
Stochastic Calculus, filtering (old stuff)Biosensors, Artificial Membranes

Statistical Signal Processing Using Matlab

Processing

Fundamentals Of Statistical Signal Processing

  • Partially Observed Markov Decision Processes book, Cambridge, 2016
  • Dynamics of Engineered Artificial Membranes & Biosensors,Cambridge, 2018.