<title>ML-blind deconvolution algorithm: recent developments</title>

Abstract

The Maximum Likelihood based blind deconvolution (ML-blind) algorithm is used to deblur three dimensional microscope images. This approach was first introduced to the microscope community by us circa 1992. The basic advantage of a blind algorithm is that it simplifies the user interface protocols and reconstructs both the object and the Point Spread Function. In this paper we will discuss the recent improvements to the algorithm that robustize the performance and accelerate the speed of convergence. For instance, powerful and physically justified constraints are enforced on the reconstructed PSF at every iteration for robustization. A line search technique is added to the object reconstruction to accelerate the convergence of the object estimate. A simple modification to the algorithm enables adaptation for the transmitted light brightfield modality. Finally, we incorporate montaging in order to process large data fields. Introduction and SignificanceMicroscope images are collected using the optical sectioning method [fl. A two dimensional (2D) data set is collected by focusing the objective lens of the microscope onto a plane of interest and capturing the image using a cooled Charged Coupled Device (CCD) camera [2]. The position of the focal plane is stepwise incremented from the bottom to the top of the sample and, each time, a 2D image frame is collected. These 2D frames are stacked one after the other to form a three dimensional (3D) data set.A 2D optical section contains both sharp features from the in-focus plane and blurred out-of-focus features from adjacent planes. Therefore, a collected 3D image displays considerable haze and blur along both the axial and lateral directions. The main purpose of a deblurring algorithm is to remove random noise and out-of-focus haze, and to restore the sharp in-focus features.The Maximum Likelthood (ML) based blind deconvolution (ML-blind) [3-6] method is a model-based deblurring approach that utilizes the iterative Estimation-Maximization (EM) technique and removes blurry out-of-focus features from a 3D microscope image. This method does not require prior knowledge of the Point Spread Function (PSF) of the system. Instead, it reconstructs the PSF and the image data simultaneously.The advantage of using the ML-blind method over other non-blind (requires a PSF) algorithms is that it simplifies the user interface protocols. To obtain an input PSF for non-blind algorithm one may measure [7]aPSF or calculate it from theoretical formulations [8], [9]. The disadvantage of measuring a microscope PSF [7] is that the details of the PSF measuring techniques are not esoteric. The disadvantages of using a theoretically calculated PSF are: 1) It contains simplified mathematical assumptions about the optics [8].2) The PSF calculation requires careful calibration of physical parameters [9] (such as depth of the sample from the cover-glass, and refractive index accuracy of the embedding medium to within three decimal places) which are tedious, and difficult to obtain for routine ...

Blind deconvolution of 3D transmitted light brightfield micrographs

“…Figures 10 and 11 show a deconvolution of a large field. The montage and acceleration schemes (Bhattacharyya et al ., 1996) that were developed in conjunction with other deconvolution research were used. The sample was a pyramidal neurone from the CA‐3 region of the hippocampus of a neonatal rat.…”