  Optic deconvolution in light microscopy (LM) refers to recovering the object
details from images, revealing the ground truth of samples. Traditional
explicit methods in LM rely on the point spread function (PSF) during image
acquisition. Yet, these approaches often fall short due to inaccurate PSF
models and noise artifacts, hampering the overall restoration quality. In this
paper, we approached the optic deconvolution as an inverse problem. Motivated
by the nonstandard-form compression scheme introduced by Beylkin, Coifman, and
Rokhlin (BCR), we proposed an innovative physics-informed neural network
Multi-Stage Residual-BCR Net (m-rBCR) to approximate the optic deconvolution.
We validated the m-rBCR model on four microscopy datasets - two simulated
microscopy datasets from ImageNet and BioSR, real dSTORM microscopy images, and
real widefield microscopy images. In contrast to the explicit deconvolution
methods (e.g. Richardson-Lucy) and other state-of-the-art NN models (U-Net,
DDPM, CARE, DnCNN, ESRGAN, RCAN, Noise2Noise, MPRNet, and MIMO-U-Net), the
m-rBCR model demonstrates superior performance to other candidates by PSNR and
SSIM in two real microscopy datasets and the simulated BioSR dataset. In the
simulated ImageNet dataset, m-rBCR ranks the second-best place (right after
MIMO-U-Net). With the backbone from the optical physics, m-rBCR exploits the
trainable parameters with better performances (from ~30 times fewer than the
benchmark MIMO-U-Net to ~210 times than ESRGAN). This enables m-rBCR to achieve
a shorter runtime (from ~3 times faster than MIMO-U-Net to ~300 times faster
than DDPM). To summarize, by leveraging physics constraints our model reduced
potentially redundant parameters significantly in expertise-oriented NN
candidates and achieved high efficiency with superior performance.
