Register to reply

LS solution vs. pre-averaging

by divB
Tags: preaveraging, solution
Share this thread:
Jan22-13, 09:10 PM
P: 87

I have a system of equations [itex]\mathbf{y} = \mathbf{A}\mathbf{c}[/itex] where the entries in [itex]\mathbf{c}[/itex] are small (say, K=10 elements) and the number equations (i.e., elements in [itex]\mathbf{y}[/itex]) is huge (say, N=10000 elements).

I want to solve now for [itex]\mathbf{c}[/itex]; this can be done using LS with the Pseudo inverse:

[tex]\mathbf{c} = \mathbf{A}^{\dagger} \mathbf{y}[/tex]

However, the vector [itex]\mathbf{y}[/itex] is now heavily corrupted by noise (just assume iid Gaussian).

I could calculate the mean over M consecutive elements in [itex]\mathbf{y}[/itex] and rows in [itex]\mathbf{A}[/itex] in order to average over the noise. The system would be collapsed to a smaller system with N/M entries which would be solved via LS.

Now I ask the question: Is this better than directly using LS with the full system?

I doubt because that's the sense of LS. However, I was not able to "proof" this analytically.

Any help?
Phys.Org News Partner Mathematics news on
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Jan22-13, 09:35 PM
P: 4,573
Hey divB.

Can you use the properties of a psuedo-inverse to show that this holds? (Recall that a pseudo-inverse has the property that C*C'*C = C)

Register to reply

Related Discussions
Matlab - averaging Math & Science Software 17
Averaging errors Precalculus Mathematics Homework 4
Averaging of velocities! Introductory Physics Homework 14
Dice Averaging Dilemna General Math 18
Signal averaging Electrical Engineering 27