How to calculate A'*A

[ZhangHuYi]

I'm a student studying CT reconstruction and recently wanted to solve the objective function using the split-bregam framework, but one of the steps was to calculate A'*A, and I wanted to ask how I could solve this problem。

[AnderBiguri]

Hi! The answer is that you can't. The matrix A is too large to be stored in memory for CBCT so Tigre never computes it explicitly. Not only that, but the transpose it's just an approximation. So, using Tigre, you can even only compute A*x or A'*b, but not just A or A'. So, you could compute A'*A*x, but not just A'*A.

[AnderBiguri]

That said, I do believe split bregman has been used for CT in a way that you don't need such matrix, but I can't remember the reference now. Check the literature.

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On Fri, 12 Jan 2024, 08:11 ander biguri, ***@***.***> wrote: Hi! The answer is that you can't. The matrix A is too large to be stored in memory for CBCT so Tigre never computes it explicitly. Not only that, but the transpose it's just an approximation. So, using Tigre, you can even only compute A*x or A'*b, but not just A or A'. So, you could compute A'*A*x, but not just A'*A.