Path: news.mathworks.com!not-for-mail
From: "Hua Wang" <ehwang@163.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: how to deal with the inversion problem of a huge sparse
Date: Mon, 28 Sep 2009 09:19:02 +0000 (UTC)
Organization: The MathWorks, Inc.
Lines: 23
Message-ID: <h9pv26$nar$1@fred.mathworks.com>
References: <h9llp6$mho$1@fred.mathworks.com> <h9o54a$pnq$1@fred.mathworks.com> <ef773a28-76ca-4e60-b6ee-dc944f4e6ba0@h30g2000vbr.googlegroups.com>
Reply-To: "Hua Wang" <ehwang@163.com>
NNTP-Posting-Host: webapp-05-blr.mathworks.com
Content-Type: text/plain; charset="ISO-8859-1"
Content-Transfer-Encoding: 8bit
X-Trace: fred.mathworks.com 1254129542 23899 172.30.248.35 (28 Sep 2009 09:19:02 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Mon, 28 Sep 2009 09:19:02 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 2007239
Xref: news.mathworks.com comp.soft-sys.matlab:573307


> 
> I haven't seen anything that indicates neither the size of
> these images in terms of pixels, or the dimensions of the
> covarinance matrices. Nor have I seen anything to indicate
> what the purpose of the analysis is.

Sorry that I forgot the pixel size. In my dataset, the original pixel size is about 90 m. It is to slow to process such high resolution data. After multilooking (i.e. average for the neighbor pixels), the pixel size is about 360 m. So there are about 300*2400 pixels for each image. After removing some pixels with NaN values, the dimension of the final covariance matrix is about 40,000 by 40,000 with 15 million non-zeros.

> Again, any desire to invert a large matrix is almost always
> wrong. In the few cases where inversion is warranted, the
> naive inversion is almost never the correct algorithm.
> 
> Of course, it could be that the OP's application is among the
> handful that remains, but it might be worth the effort to
> investigate alternative algorithms.

In my study, I got deformation from different radar images. Because of different geometry of the radar images, the deformation field is not continuous from one image to the other. My idea is to divide my study area into triangular mesh, and invert the velocities on the nodes of the mesh using all radar data. If I know the radar geometry, it is reasonable to solve it.

I am also thinking to use cleverer algorithm, e.g. dividing the image into different patches. But I some parameters, e.g. orbital errors of the radar image, should be the same for the patches within a image. I am not clear how to add such constraints if I use patch strategy. Alternatively, could you give me some suggestions? 

Thanks a lot!

Hua