Introduction (without the movies)
Question set 1 - Due April 19
Question set 2 - Due May 10
Question set 3, lena.png - Due June 21
All of the subjects learned in class and a few more are summarized here:
M. Unser, "Sampling - 50 years after shannon," IEEE Proc., vol. 88 pp. 569-587, Apr. 2000.
Y. C. Eldar and T. Michaeli, "Beyond bandlimited sampling," IEEE Signal Processing Magazine, vol. 26, no. 3, pp. 48-68, May 2009.
T. Michaeli and Y. C. Eldar, "Optimization techniques in modern sampling theory," to appear in Convex Optimization in Signal Processing and Communications, Edited by Y. C. Eldar and D. Palomar, Cambridge University Press.
Proof of the direct-sum characterization theorem
Each student should pick a subject from the list bellow or contact us to define a project related to his/her work or research.
The final project will consist of the following:
Implementing the algorithm proposed in the paper and testing it in various scenarios. The documented Matlab code is to be submitted.
Writing a 4-page critical summary on the paper in a conference-style format. The summary should focus mainly on the attributes of the algorithm as exposed by the simulations you implemented. Improvements should be proposed in one or more of the following contexts:
Algorithmic improvements
Efficient implementations
Theoretical analysis
Offering a new viewpoint on the subject using tools learned in class
Demonstrating the algorithm in the context of applications not mentioned in the original article (speech, images, communication, etc.)
Preparing a 15 minutes presentation, in which you will present the main idea of the paper and talk about your improvements.
The critical summary along with the code should be submitted by June 28. The presentations will take place at the last two weeks of the semester, namely June 28th and July 5th, during class.
Word and Latex templates for writing a conference-style summary (taken from ICASSP 08):
LaTeX style file with margin, page layout, font, etc. definitions.
LaTeX template file, an example of using the "spconf.sty" and "IEEEbib.bst" files above.
Sample strings.bib and refs.bib files.
Word 97/2000 Sample, a template of correct formatting and font use.
June 28:
Compressed sensing
Michal Genussov
Eli OsherovichShifted interpolation in SI spaces
Yael Yankelevsky
Noam WagnerNonlinear distortion
Yoni Bahat
Tomer Factor
July 5:
Oversampling in SI spaces
David Ben-Haim
Igor TzelnikerInterleaved A/D
Ran Marom
High rate interpolation
Michael Farid
Feedback loop correction
Yaara David
Quantization in SI spaces
Asaf Elron
"Linear interpolation revitalized"
The method in the paper should be implemented. Subjects to be addressed:
Extending the algorithm to other SI spaces.
Devising a method for finding the optimal shift without relying on approximation theory.
"Sampling models for linear time-variant filters"
The sampling formulae should be implemented. Subjects to be addressed:
Demonstrating the methods on synthetic signals.
Extending the formulae to general SI spaces.
"The recovery of distorted band-limited stochastic processes", "The recovery of distorted band-limited signals"
The theoretical results of both papers should be summarized and the algorithm in the second one should be implemented. Subjects to be addressed:
Comparison with the algorithm learned in class (in terms of convergence rate, simplicity, etc.).
Extension to general SI spaces (at least the uniqueness proof in the second paper).
"Single disperser design for coded aperture snapshot spectral imaging", "Compressive coded aperture superresolution image reconstruction"
The methods of both papers should summarized and the algorithm in the second one should be implemented. Subjects to be addressed:
Demonstrating the method on images.
Testing the effect of the dictionary on the reconstruction.
"High rate interpolation of random signals from nonideal samples"
The method should be implemented and specialized to spline spaces. Subjects to be addressed:
Efficient implementation in spline spaces using causal and anti-causal IIR filters, similar to homework assignments 2 and 3.
Comparison with standard spline interpolation in terms of recovery error and complexity.
The method should be implemented. Subjects to be addressed:
Study the behavior of the proposed algorithm via simulations.
Apply the algorithm to super-resolution of image sequences (contact us for information).
Quantization of a sampled signal can be regarded as adding white noise to the sequence of samples. If the original signal is known to occupy only a fraction of the Nyquist bandwidth, then part of the quantization noise spectra can be zeroed out when reconstructing the signal. This is a well known tradeoff between the sampling-rate and quantization-step. In this project, you are required to extend this result to general shift invariant spaces (namely not necessarily bandlimited signals). Subjects to be addressed:
Analysis of the case where the sampling filter matches the signal prior.
Analysis of the case where the sampling filter does not match the signal prior.
Demonstration of the results in the context of audio/image interpolation with splines and other common methods.
As learned in class, in order to consistently recover a signal lying in a shift-invariant space, we need to digitally filter the samples prior to reconstruction with a kernel that generates this space. In homework assignment 2 we saw that in some cases this digital filtering block can be implemented as a concatenation of simple IIR filters. In this project you are required to implement this block in an iterative manner using a closed loop feed-back. Specifically, using the fact that
(S*W)-1 = I - (S*W-I) + (S*W-I)2 - (S*W-I)3 + (S*W-I)4 + ... ,
we can implement the filtering stage using a negative feedback of (S*W-I). Subjects to be addressed:
Comparison with the standard approach in spline interpolation, in terms of complexity and resulting error (for a fixed number of iterations).
Demonstration of the results in the context of audio/image interpolation with splines and other common methods.
Please contact us for details.
