S-114.4220 Research Seminar on Computational Science
	TKK / Units / LCE / Teaching / Courses / S-114.4220 / k2008

The topic of the course in 2008 spring (period IV) is

Stochastic Models in Spatial and Image Analysis (3 p) L V

The topic will cover, e.g.,

• Connection between image analysis and spatial modeling (kriging)
• Connection between Gaussian processes, Wiener-filters, Gaussian Markov Random fields, other Markov and non-Markov hidden and non-hidden random fields, and wavelet analysis.
• Wiener filter and its connection to Gaussian process regression and Kalman filters and RTS smoothers.
• FFT and FIR approximations to speed up Wiener filters and GP regression
• Image compression, e.g., wavelet-based compression in JPEG2000

Literature

• T. F. Chan, J. Shen (2005): Image Processing and Analysis: Variational, PDE, Wavelet and Stochastic Methods
• B. Finkenstädt, L. Held, V. Isham (2006): Statistical Methods for Spatio-Temporal Systems
• M.A.R. Ferreire, H.K.H. Lee (2007): Multiscale Modeling - A Bayesian perspective.
• Lim (1989): Two-Dimensional Signal and Image Processing
• Gonzalez and Woods (2002): Digital Image Processing
• Christakos (1992): Random Field Models in Earth Sciences
• H. L. Van Trees (1968): Detection, Estimation, and Modulation Theory Part I

Teachers

Dr.Tech. Simo Särkkä, Docent, Dr.Tech. Aki Vehtari

Prerequisites

Basics of Bayesian inference and matrix algebra. Basic knowledge or ability to learn to use Matlab is needed for completing the exercise.

Place and time

The seminars take place on Wednesdays at 14:15 in Innopoli 2, B317 (the seminar room of Laboratory of computational engineering, see map) First lecture is 26.3. 14:15.

Course Registration

Please register for the course by sending email to Aki.Vehtari@hut.fi. Remember to mention the student id. If you have an suggestion for the topic of your presentation, you may mention it in the email also.

Language

English if at least one English speaking participant.

Schedule

General instructions

In every seminar talk, there is the author who writes a 2-4 page summary paper about the subject and gives the talk, and an opponent, whose task is to make questions and stimulate discussion after the presentation. Every student is the author for (at least) one talk and the opponent for another talk. The author should send the summary paper to the opponent and to the teachers on the monday preceding the presentation day. The slides should be sent to the teacher latest on the day preceding the presentation. The opponent prepares at least 2-3 questions about the topic to stimulate discussion after the talk. Normal talk is 30-40 minutes.

Exercise:

In the computer exercise, you should apply Wiener filter, median filter and a freely chosen third method for removing different kinds of noises and degradations from image and compare the results. The exercise report should be returned in PDF format to the e-mail address ssarkka@lce.hut.fi, not later than 16.6.2008.

You can choose any gray scale test image you want. One possible choice is the use the classical Lena (Lenna) image, whose story can be found here:

http://en.wikipedia.org/wiki/Lenna

Gray scale versions of the image can be found by typing "lenna image" into the google. With the image, you should do the following:

1. Generate a noisy image by adding additive Gaussian noise with a given covariance function to the image and another image by adding salt-and-pepper shot noise to the image.
2. By investigating the covariance function of the original image, choose couple of candidate covariance functions to be used in the Wiener filter. Also compute the Fourier transforms of the covariance functions that you have chosen.
3. Design Wiener filters, which correspond to the choices of covariance functions, and which can be used for removing the noises from the images. Implement the filters in Matlab using FFT2 algorithm. Remember to take into account and eliminate the usual border effects caused by the circular convolution of FFT algorithm.
4. Compare the results of the Wiener filters and median filter (medfilt2 in Matlab) with both types of noise in images.
5. Compare the noise removal results to some freely chosen alternative method. You can, for example, use a Wavelet based method, variational method, stochastic relaxation or some other method that you find appropriate.
6. Construct a convolution filter, which approximates a simple motion blur of the image. Using one of the covariance functions above, construct a Wiener filter for removing the motion blur and noise from the image. Test the performance of the filter in Matlab.
7. How long does the filtering operation take and what is the computational complexity of the Wiener filter with respect to the size of the image? If the direct Gaussian process regression equations were used in the computation, approximately how long would the computations take and what would be the computational complexity in this case?

Contact:

When sending email concerning the course, please add "S-114.4220" or "1144220" to subject.

Dr.Tech. Simo Särkkä
ssarkka@lce.hut.fi
http://www.lce.hut.fi/~ssarkka/

Docent, Dr.Tech. Aki Vehtari
Aki.Vehtari@hut.fi
http://www.lce.hut.fi/~ave/