Could I obtain the deconvolved image if I have an original image and its PSF? And if I have a deconvolved image and its PSF, how can I obtain the convolved image?

Convolution, see for images

is basically. a matrix multiplication, so your second part is relatively easy.

The inverse operation is not uniquely determined, you are facing an inverse problem, so that can not be done in a stable way (without â€śtricksâ€ť like regularisation).

Tikhonov regularization is pretty common for this kind of problem, a version of which (if you have some estimate of the spectral density) is called Wiener deconvolution. (These can be implemented with FFTs.) This works pretty well in my experience if the noise is relatively small and the PSF is not too blurry.

Tikhonov sometimes gets a bit blurry, but you can also do TV-regularization (Total variation denoising - Wikipedia) as a regulariser. This usually keeps edges â€“ and is more often used in (pure) denoising and not necessarily deconvolution.

Have you looked at the Julia package: DeconvOptim.jl?

Thank you, this works well

Author here, if you need some assistance, feel free to ping me

Thank you. The tutorial is clear on website and youtube