Gaussian mixture models for spots in microscopy using a new split/merge em algorithm

Pan, Kangyu; Kokaram, Anil; Hillebrand, Jens; Ramaswami, Mani

doi:10.1109/icip.2010.5652472

Cited by 5 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, we need to find a β > 0 such that ∇g is β −1 -Lipschitz continuous, and provide a way to compute prox γ f (a) for any γ > 0 and a ∈ A. We start by characterizing the behavior of the smooth function g in (5). The result in Property 1 follows finite-dimensional intuition and specifies this behavior completely.…”

Section: B Accelerated Proximal Gradient For Weighted Group-sparse-rmentioning

confidence: 99%

See 1 more Smart Citation

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity—Part II: Proximal Optimization and Performance Evaluation

Aguila

Jaldén

2018

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this second part, we focus on our algorithmic contributions. We provide an algorithm for functional inverse diffusion that solves the variational problem we posed in Part I. As part of the derivation of this algorithm, we present the proximal operator for the non-negative group-sparsity regularizer, which is a novel result that is of interest in itself, also in comparison to previous results on the proximal operator of a sum of functions. We then present a discretized approximated implementation of our algorithm and evaluate it both in terms of operational cell-detection metrics and in terms of distributional optimal-transport metrics.

show abstract

Section: B Accelerated Proximal Gradient For Weighted Group-sparse-rmentioning

confidence: 99%

“…Property 1: (Fréchet derivative of the squared-norm loss). Consider the functional g : D → R in (5). Then, g has a Frchet derivative ∇g :…”

Section: B Accelerated Proximal Gradient For Weighted Group-sparse-rmentioning

confidence: 99%

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity—Part II: Proximal Optimization and Performance Evaluation

Aguila

Jaldén

2018

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…This image was obtained from a biochemical assay in which FITC dye was used as a marker, and it was captured by an RGB sensor that produced raw data with dimensions M = N = 2048 and a dynamic range of [0, 2 16 − 1]. This raw data was subject to a Bayer color filter array [54], in which neighboring pixels correspond to different color bands.…”

Section: A Example On Real Datamentioning

confidence: 99%

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity—Part I: Modeling and Inverse Problems

Aguila

Jaldén

2018

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

In this two-part paper, we present a novel framework and methodology to analyze data from certain imagebased biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs' Green function to derive a novel parametrization of the acquired images. This parametrization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a non-negative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology.

show abstract

“…Some approaches have been presented to specifically deal with the problem of particles in close proximity. The approaches in [13] and [16] fit a mixture of Gaussian models for detecting close and overlapping spots. To cope with the problem of particles in close proximity, an approach based on an adaptive h-dome transform has been described in [17].…”

mentioning

confidence: 99%

Tracking Virus Particles in Fluorescence Microscopy Images Using Multi-Scale Detection and Multi-Frame Association

Jaiswal

Godinez

Eils

et al. 2015

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

Automatic fluorescent particle tracking is an essential task to study the dynamics of a large number of biological structures at a sub-cellular level. We have developed a probabilistic particle tracking approach based on multi-scale detection and two-step multi-frame association. The multi-scale detection scheme allows coping with particles in close proximity. For finding associations, we have developed a two-step multi-frame algorithm, which is based on a temporally semiglobal formulation as well as spatially local and global optimization. In the first step, reliable associations are determined for each particle individually in local neighborhoods. In the second step, the global spatial information over multiple frames is exploited jointly to determine optimal associations. The multi-scale detection scheme and the multi-frame association finding algorithm have been combined with a probabilistic tracking approach based on the Kalman filter. We have successfully applied our probabilistic tracking approach to synthetic as well as real microscopy image sequences of virus particles and quantified the performance. We found that the proposed approach outperforms previous approaches.

show abstract

Gaussian mixture models for spots in microscopy using a new split/merge em algorithm

Cited by 5 publications

References 6 publications

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity—Part II: Proximal Optimization and Performance Evaluation

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity—Part II: Proximal Optimization and Performance Evaluation

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity—Part I: Modeling and Inverse Problems

Tracking Virus Particles in Fluorescence Microscopy Images Using Multi-Scale Detection and Multi-Frame Association

Contact Info

Product

Resources

About