Statistical signal processing is an indispensable technology in processing of signal containing noise, and widely utilized in various fields, such as information communication, measurement and control systems, imaging, voice, and medical field.
Based on the knowledge of linear algebra and statistics learned in previous lectures, this course deals with the mathematical theory that is necessary for advanced signal and image processing.
Topics include the probabilistic model of noise, statistical meaning of least square estimate, maximum-likelihood estimation, Bayesian estimation, EM algorithm and linear dynamical systems.
Through the lectures, the students will be able to:
1) Understand basis of statistical signal processing theory such as linear estimation method and maximum likelihood estimation.
2) Learn the parameter estimation technique for observation system containing statistical noise and be applied the technique to the information communication engineering research.
Random vector, probability distribution function, linear inverse problem, maximum likelihood estimate, linear least square estimation, regularization, ill-conditioned system, Bayesian estimation, EM algorithm, Kalman filter
✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Two lectures are given in every week.
Course schedule | Required learning | |
---|---|---|
Class 1 | Statistics in signal processing | Why is statistics necessary in signal processing? |
Class 2 | Random vectors, multivariate probability distribution, multidimensional normal distribution | Represent signal and noise with random variables. Derive the statistics of linearly transformed random variables. Explain the meaning of the eigenvalue decomposition of the covariance matrix in a multidimensional normal distribution. |
Class 3 | Estimation of unknown quantities, maximum likelihood estimate | Estimate the statistics of a random vector by maximum likelihood principle. |
Class 4 | Linear inverse problem and least square method | Derive the least square solution in the linear inverse problem. |
Class 5 | Noise response | Derive the error in the least square solution when observed data contain noise. |
Class 6 | Estimate using regularization | Explain estimation methods that are robust against noise. |
Class 7 | Estimation in ill-conditioned system | What is the minimum-norm estimate? |
Class 8 | Bayesian estimation | Understand the relationship between prior distribution and posterior distribution and explain the difference between a Bayesian estimation and a maximum likelihood estimation. |
Class 9 | Bayesian linear regression | Explain the relationship between a least-squares solution and a Bayesian solution. |
Class 10 | Wiener filter and estimation | Explain the relationship between a Wiener filter and a statistical estimation method. |
Class 11 | EM algorithm in a linear system | Explain a statistical parameter estimation method, where the model depends on unobserved variables. |
Class 12 | Linear prediction | Estimate the linear prediction model for time series data. |
Class 13 | Spectrum estimation | Estimate spectral information of time series data using the model estimated by the linear prediction. |
Class 14 | Kalman filter | Estimates of unknown variables from series of measurements observed over time, containing statistical noise. |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Kensuke Sekihara, Introduction to statistical signal processing, KYORITSU SHUPPAN CO., LTD.
Handouts will be distributed in each class.
Grading is made based on in-class quizzes and homework assignments, 1st report for basics of the statistical signal processing, and 2nd report for the Bayesian estimation and its application.
ICT.M202 (Probability and Statistics (ICT)), ICT.S302 (Functional Analysis and Inverse Problems) is desired.