Rapid deconvolution of low-resolution time-of-flight data using Bayesian inference

The deconvolution of low-resolution time-of-flight data has numerous advantages, including the ability to extract additional information from the experimental data. We augment the well-known Lucy-Richardson deconvolution algorithm using various Bayesian prior distributions and show that a prior of second-differences of the signal outperforms the standard Lucy-Richardson algorithm, accelerating the rate of convergence by more than a factor of four, while preserving the peak amplitude ratios of a similar fraction of the total peaks. A novel stopping criterion and boosting mechanism are implemented to ensure that these methods converge to a similar final entropy and local minima are avoided. Improvement by a factor of two in mass resolution allows more accurate quantification of the spectra. The general method is demonstrated in this paper through the deconvolution of fragmentation peaks of the 2,5-dihydroxybenzoic acid matrix and the benzyltriphenylphosphonium thermometer ion, following femtosecond ultraviolet laser desorption

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Semi-Blind Spatially-Variant Deconvolution in Optical Microscopy with Local Point Spread Function Estimation By Use Of Convolutional Neural Networks

We present a semi-blind, spatially-variant deconvolution technique aimed at optical microscopy that combines a local estimation step of the point spread function (PSF) and deconvolution using a spatially variant, regularized Richardson-Lucy algorithm. To find the local PSF map in a computationally tractable way, we train a convolutional neural network to perform regression of an optical parametric model on synthetically blurred image patches. We deconvolved both synthetic and experimentally-acquired data, and achieved an improvement of image SNR of 1.00 dB on average, compared to other deconvolution algorithms.Comment: 2018/02/11: submitted to IEEE ICIP 2018 - 2018/05/04: accepted to IEEE ICIP 201

Least-squares methods with Poissonian noise: an analysis and a comparison with the Richardson-Lucy algorithm

It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is, in large part, Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information will be more effective than those that do not. The Richardson-Lucy (RL) algorithm, for example, can be viewed as a maximum-likelihood (ML) method for image deblurring when the data noise is assumed to be Poissonian. Least-squares (LS) approaches, on the other hand, arises from the assumption that the noise is Gaussian with fixed variance across pixels, which is rarely accurate. Given this, it is surprising that in many cases results obtained using LS techniques are relatively insensitive to whether the noise is Poissonian or Gaussian. Furthermore, in the presence of Poisson noise, results obtained using LS techniques are often comparable with those obtained by the RL algorithm. We seek an explanation of these phenomena via an examination of the regularization properties of particular LS algorithms. In addition, a careful analysis of the RL algorithm yields an explanation as to why it is more effective than LS approaches for star-like objects, and why it provides similar reconstructions for extended objects. We finish with a convergence analysis of the RL algorithm. Numerical results are presented throughout the paper. It is important to stress that the subject treated in this paper is not academic. In fact, in comparison with many ML algorithms, the LS algorithms are much easier to use and to implement, often provide faster convergence rates, and are much more flexible regarding the incorporation of constraints on the solution. Consequently, if little to no improvement is gained in the use of an ML approach over an LS algorithm, the latter will often be the preferred approach.Comment: High resolution images are available upon request. submitted to A&

Adaptive Optimized Discriminative Learning based Image Deblurring using Deep CNN

Image degradation plays a major problem in many image processing applications. Due to blurring, the quality of an image is degraded and there will be a reduction in bandwidth. Blur in an image is due to variations in atmospheric turbulence, focal length, camera settings, etc. Various types of blurs include Gaussian blur, Motion blur, Out-of-focus blur. The effect of noise along with blur further corrupts the captured image. Many techniques have evolved to deblur the degraded image. The leading approach to solve various degraded images are either based on discriminative learning models or on optimization models. Each method has its own advantages and disadvantages.  Learning by discriminative methods is faster but restricted to a specific task whereas optimization models handle flexibly but consume more time. Integrating optimization models suitably by learning with discriminative manner results in effective image restoration. In this paper, a set of effective and fast Convolutional Neural Networks (CNNs) are employed to deblur the Gaussian, motion and out-of-focus blurred images that integrate with optimization models to further avoid noise effects. The proposed methods work more efficiently for applications with low-level vision