Marginal blind deconvolution of adaptive optics retinal images

Abstract

Adaptive Optics corrected flood imaging of the retina has been in use for more than a decade and is now a well-developed technique. Nevertheless, raw AO flood images are usually of poor contrast because of the three-dimensional nature of the imaging, meaning that the image contains information coming from both the in-focus plane and the out-of-focus planes of the object, which also leads to a loss in resolution. Interpretation of such images is therefore difficult without an appropriate post-processing, which typically includes image deconvolution. The deconvolution of retina images is difficult because the point spread function (PSF) is not well known, a problem known as blind deconvolution. We present an image model for dealing with the problem of imaging a 3D object with a 2D conventional imager in which the recorded 2D image is a convolution of an invariant 2D object with a linear combination of 2D PSFs. The blind deconvolution problem boils down to estimating the coefficients of the PSF linear combination. We show that the conventional method of joint estimation fails even for a small number of coefficients. We derive a marginal estimation of the unknown parameters (PSF coefficients, object Power Spectral Density and noise level) followed by a MAP estimation of the object. We show that the marginal estimation has good statistical convergence properties and we present results on simulated and experimental data.

Robust Multi-Frame Adaptive Optics Image Restoration Algorithm Using Maximum Likelihood Estimation with Poisson Statistics

“…The noise in an AO image is mainly photon noise that has a Poisson distribution. However, an AO astronomy image is dominated by a quite homogeneous background [23,24]. The intensity convolution based on the Shell theorem describes the non-coherent imaging system, the object image $\left\{o\right(a,b),(a,b)\in \Omega \}$ which is a nonnegative function, and the PSF $\{h_k\left((x,y)\right|(a,b)),(x,y)\in D\}$ ( D is the region of the observed image) which is affected by atmospheric turbulence.…”

“…The ML estimator based on Poisson distribution can be expressed as [23,25] $p\left(i_k(x,y)\right|o,h_k)=\frac{true\sum _{(x,y)\in \Omega }{\left(o(x,y)h_k(x,y)\right)}^{i_k(x,y)}}{true\prod _{k=1}^M{i}_k(x,y)}\times prefixexp(-{\displaystyle \sum _{(x,y)\in \Omega }}o(x,y)h_k(x,y)).$…”

Adaptive optics imaging of retinal microstructures: Image processing for medical applications

“…As fl systems usually produce noisy images mak structures hardly visible, a commonly use register these images and average them signal-to-noise ratio. Myopic deconvolutio has improved the quality of flood-illumina [4] since it enables to extract cone mosaic non-averaged) images (Figure 2), hence a related to photoreceptor scintillation an image processing. Sub-pixellic registration one of us [5] also had a significant impact image quality, through the suppression rotational artifacts ( Figure 3) and hence en over which photoreceptors can be counted.…”

Deblurring adaptive optics retinal images using deep convolutional neural networks

“…Therefore, ordinary non-blind deconvolution algorithm is not a suitable method for post-processing of AO images [5]. Thus, a more generalized technique named blind deconvolution has been proposed to restore the AO retinal images [6][7][8][9]. This type of image deconvolution allows for recovery of the retinal images and the PSF distributions simultaneously by physical constraints about the target and the PSF.…”