How does radius of point spread function affect reconstruction errors?

In summary, the individual is struggling with a concept involving the use of a gaussian blur and gaussian white noise to compute a naive solution for a blurred image. They have found a solution in their textbook that involves using periodic boundary conditions and computing eigenvalues using fast Fourier transforms. However, they have noticed that at larger blur radii, their solution has more noise and are seeking help in understanding why this happens. They postulate that it may be due to a decrease in signal-to-noise ratio per pixel and an increase in total noise added to each calculation.
  • #1
cp05
11
0
Hi guys,
I've been struggling with this concept for a few days now.
I have this *good* image that I am blurring (using a gaussian blur), then adding some small percentage of gaussian white noise to it. Then from that image, I want to compute the naive solution (just assuming B=AX and solving for X...where B is the blurred image I created and X is the *good* image, with A being the matrix that takes into account this gaussian point spread function).

I have a handy dandy textbook that says that if I use periodic boundary conditions (which I am), then I can just use the point spread function and don't ever have to construct A (yay!). I do this by computing the eigenvalues of A using fast Fourier transforms (not sure how those work either...but I guess that's a different question for a different time), then using the inverse fast Fourier transform to solve for X using the blurred matrix and those eigenvalues of A.

All great!

By playing around with the radius of my gaussian blur...I notice that at larger gaussian blur radii (ad same % of white noise), my resulting naive X solution has a lot more noise! So I was wondering if anyone can help me figure out why this happens. Why am I getting more noise in my solution with larger radii of blur...because I am not changing the % of white noise at all!

If someone could help, or point me in the right direction, I would be ever grateful.
Thanks!
 
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  • #2
Random guess, but wouldn't the larger blur mean less SNR per pixel and more total noise that is added to each calculation since you have the PSF spread over more pixels?
(I hope that makes sense. My only knowledge of this subject comes from my astrophotography)
 

Related to How does radius of point spread function affect reconstruction errors?

Question 1: What is a point spread function (PSF)?

A point spread function is a mathematical representation of the blurring or spreading of a single point of light as it passes through an imaging system, such as a microscope or a telescope.

Question 2: How does the radius of the point spread function affect reconstruction errors?

The radius of the point spread function directly affects the resolution of an image. A smaller radius results in a sharper image, while a larger radius leads to a more blurred image. This can result in reconstruction errors, as the accuracy of the image is dependent on the size of the PSF.

Question 3: How does the reconstruction method impact the relationship between PSF radius and reconstruction errors?

The reconstruction method used can affect the relationship between PSF radius and reconstruction errors. Some methods may be more sensitive to changes in PSF radius and result in higher reconstruction errors, while others may be more robust and able to produce accurate reconstructions even with larger PSF radii.

Question 4: What factors can influence the radius of the point spread function?

The radius of the point spread function can be influenced by various factors, including the quality of the imaging system, the wavelength of light used, and any aberrations or distortions in the system. Additionally, the type of sample being imaged can also affect the PSF radius.

Question 5: How can the radius of the point spread function be minimized to reduce reconstruction errors?

To minimize the radius of the point spread function, it is important to use high-quality imaging systems and to correct for any aberrations or distortions. Additionally, using shorter wavelengths of light and optimizing the imaging conditions can also help reduce the PSF radius and improve image resolution and accuracy.

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