Stanford EE 392J - Study Guide (2 pages)

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Study Guide



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Study Guide

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Problems/Exams


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2
School:
Stanford University
Course:
Ee 392j - Digital Video Processing

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Digital Video Processing EE392J Department of Electrical Engineering Stanford University Problem Set No 5 Issued Wednesday February 21 2007 Due Wednesday February 28 2007 Brief Oral Project Descriptions Wednesday February 28 2007 see next page Office hours Wed 2 21 and Mon 2 26 after class and Friday 2 23 2 00 3 00 Please feel free to stop by office hours to talk about possible projects Problem l Constraint based Signal Recovery POCS when each constraint is a subspace This problem considers constraint based signal recovery in the special case where each constraint corresponds to a subspace Assume that the desired solution satisfies a linear equation of the form a1 x1 a2 x2 aN xN 0 This equation can be equivalently expressed as aT x 0 where a a1 a2 aN T and x x1 x2 xN T RN Therefore the solution must lie in the N 1 dimensional subspace defined by aT x 0 a Determine an expression that describes how to compute the orthogonal projection of an arbitrary point x onto the subspace The orthogonal projection of an arbitrary point x onto a subspace is the point in the subspace that is closest in Euclidean distance to the point x Hint Think projection theorem or least squares b Assume that the desired solution satisfies two linear equations of the type shown above Also assume that the corresponding subspaces intersect Is there a unique solution If not what is the form of the solution e g what is its dimension c Assume you perform alternating orthogonal projections to determine an element in the solution set How does the convergence rate depend on the angle between the subspaces Hint Consider the analogous case of two 1 D subspaces in a 2 D space i e when you have two linear equations in two unknowns What happens when the subspaces are orthogonal What happens when the angle between them is very small See Back Problem 2 Brief Oral Project Description The goal of this brief presentation is twofold 1 to describe to your classmates what you are working on for your final project and



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