# What's the Difference between Convolution Kernel and Point Spread Function in the Context of Image Convolution?

When you use the deconvolution method to make the blurry image sharper, you will have to estimate the Point Spread Function. Is there a difference between this PSF and an image kernel?

Second question: Is the Point Spread Function in the time domain or frequency domain? Or can it be in both?

There is a slight difference in definition and in context. A PSF does not need to be a convolution kernel, however, it is almost always assumed to be one. Usually, you talk of a ,,PSF'' when you want to find out what it is, exactly, and of a ,,convolution kernel'' when you're aware that there is a convolution.

• So, they are the same in the context of convolution and deconvolution? – Teede Jan 3 '14 at 11:25

They are the same in the context of convolution and deconvolution. But PSF is only one of the kernels used in convolution/deconvolution.

Besides, since it is not easy to get an accurate PSF, or probably even cannot get one, PSF sometimes is not directly used in deconvolution. Some regularization factors referring to noise is often added, as a form of wiener deconvolution.

In the presence of a poorly determined or unknown, blind deconvolution is also used with an initial guess of PSF and gradually approximating it. Note in blind deconvolution sometimes it doesn't estimate and apply P(oint)SF, but L(ine)SF in cross section acquisition (B-mode ultrasound image for example). Yet the images from most optical sensors apply PSF.

PSF is the system response to a point source, and it is mostly measured in spatial domain. When you implement the convolution/deconvolution, you may often transform the image and PSF to frequency domain to do the multiplication/dividing equivalently.

• What do you mean with "PSF sometimes is not directly used in deconvolution"? I think you can use PSF for wiener deconvolution. This is also mentioned here: mathworks.com/help/images/examples/… And Ultrasound? I meant images from a normal camera. – Teede Jan 3 '14 at 15:01
• Thank you Teede. Yes that is what I mean. You need to consider the impact of SNR in deconvolution, so instead of using only PSF, you use PSF plus some regularization factor to form the wiener filter. Besides,I just took an ultraound image for example to show that sometimes line spread function is used in deconvolution rather than point spread function. Of course the images from most optical sensors apply PSF. – lennon310 Jan 3 '14 at 15:19
• update my answer, thx – lennon310 Jan 3 '14 at 15:24
• Thanks! Second question: Is the Point Spread Function in the time domain or frequency domain? Or can it be in both? – Teede Jan 3 '14 at 15:28
• Thanks! Found this on wikipedia as well: "A transfer function is the Fourier transform of the point spread function" en.wikipedia.org/wiki/Transfer_function – Teede Jan 5 '14 at 22:17

The PSF (Point Spread Function) is the system response to Impulse Signal (Point).

If your system model is LSI (Linear Spatially Invariant) then the output image of the system is applying the PSF as a convolution kernel on the input image.

Yet, the PSF is just the response of a system to a certain input.
It doesn't describe the whole system unless it is an LSI system.

If you model for the Deconvolution problem (Often called the Degradation Model) is LSI, then what you estimate is indeed the PSF.