The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform

Yue Wang - One of the best experts on this subject based on the ideXlab platform.

  • Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources.
    Scientific reports, 2016
    Co-Authors: Yitan Zhu, Niya Wang, David J. Miller, Yue Wang
    Abstract:

    Blind Source Separation (BSS) is a powerful tool for analyzing composite data patterns in many areas, such as computational biology. We introduce a novel BSS method, Convex Analysis of Mixtures (CAM), for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the Convex data scatter plot. We propose and prove a sufficient and necessary condition for identifying the mixing matrix through edge detection in the noise-free case, which enables CAM to identify the mixing matrix not only in the exact-determined and over-determined scenarios, but also in the under-determined scenario. We show the optimality of the edge detection strategy, even for cases where source well-groundedness is not strictly satisfied. The CAM algorithm integrates plug-in noise filtering using sector-based clustering, an efficient geometric Convex Analysis scheme, and stability-based model order selection. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data of ovarian cancer subtypes. We apply CAM to dissect dynamic contrast-enhanced magnetic resonance imaging data taken from breast tumors and time-course microarray gene expression data derived from in-vivo muscle regeneration in mice, both producing biologically plausible decomposition results.

  • Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources
    arXiv: Machine Learning, 2014
    Co-Authors: Yitan Zhu, Niya Wang, David J. Miller, Yue Wang
    Abstract:

    Blind Source Separation (BSS) has proven to be a powerful tool for the Analysis of composite patterns in engineering and science. We introduce Convex Analysis of Mixtures (CAM) for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the Convex data scatter plot. We prove a sufficient and necessary condition for identifying the mixing matrix through edge detection, which also serves as the foundation for CAM to be applied not only to the exact-determined and over-determined cases, but also to the under-determined case. We show the optimality of the edge detection strategy, even for cases where source well-groundedness is not strictly satisfied. The CAM algorithm integrates plug-in noise filtering using sector-based clustering, an efficient geometric Convex Analysis scheme, and stability-based model order selection. We demonstrate the principle of CAM on simulated data and numerically mixed natural images. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data. We then apply CAM to dissect dynamic contrast-enhanced magnetic resonance imaging data taken from breast tumors and time-course microarray gene expression data derived from in-vivo muscle regeneration in mice, both producing biologically plausible decomposition results.

  • A Convex Analysis Framework for Blind Separation of Non-Negative Sources
    IEEE Transactions on Signal Processing, 2008
    Co-Authors: Tsung-han Chan, Chong-yung Chi, Yue Wang
    Abstract:

    This paper presents a new framework for blind source separation (BSS) of non-negative source signals. The proposed framework, referred herein to as Convex Analysis of mixtures of non-negative sources (CAMNS), is deterministic requiring no source independence assumption, the entrenched premise in many existing (usually statistical) BSS frameworks. The development is based on a special assumption called local dominance. It is a good assumption for source signals exhibiting sparsity or high contrast, and thus is considered realistic to many real-world problems such as multichannel biomedical imaging. Under local dominance and several standard assumptions, we apply Convex Analysis to establish a new BSS criterion, which states that the source signals can be perfectly identified (in a blind fashion) by finding the extreme points of an observation-constructed polyhedral set. Methods for fulfilling the CAMNS criterion are also derived, using either linear programming or simplex geometry. Simulation results on several data sets are presented to demonstrate the efficacy of the proposed method over several other reported BSS methods.

  • ISBI - Convex Analysis and separation of composite signals in DCE-MRI
    2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008
    Co-Authors: Li Chen, Tsung-han Chan, Chong-yung Chi, Peter L. Choyke, Ge Wang, Yue Wang
    Abstract:

    Dynamic functional imaging promises powerful tools for the visualization and elucidation of important disease- causing biological processes, where the pixels often represent a composite of multiple biomarkers independent of spatial resolution. This study exploits both blind source separation and imagery marker characteristics to develop a hybrid method for the separation of mixed yet correlated biomarker distributions in DCE-MRI. A compartment latent variable model is constructed upon which a novel Convex Analysis framework is proposed to provide a close-form algebraic solution to separating composite markers with non-negativity and well-grounded points. A unique non- negative clustered component Analysis is further developed to explicitly consider both partial volume effect and noise contamination. Experimental results show promising and robust extraction of time activity curves and vascular marker images in agreement with biomedical expectations.

  • Convex Analysis for separation of functional patterns in DCE-MRI: A longitudinal study to antiangiogenic therapy
    2008 IEEE Workshop on Machine Learning for Signal Processing, 2008
    Co-Authors: Tsung-han Chan, Chong-yung Chi, Li Chen, P.l. Choyke, Yue Wang
    Abstract:

    Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can characterize vascular heterogeneity, and has potential utility in assessment of the efficacy of angiogenesis inhibitors in cancer treatment. Due to the heterogeneous nature of tumor microvasculature, the measured signals can be represented as the mixture of the permeability images corresponding to different perfusion rates. We recently reported a hybrid Convex Analysis of mixture framework for unmixing of non-negative yet dependent angiogenic permeability distributions (APDs) and perfusion time activity curves (TACs). In our last work, we presented an underlying theory to infer the concept that the TACs can be identified by finding the lateral edges of an observation-constructed Convex pyramid when the well-grounded points exist for all APDs. For fulfilling this concept, a hybrid method including non-negative clustered component Analysis, Convex Analysis, and least-squares fitting with non-negativity constraints was developed. In this paper, we use computer simulations to validate the performance of our reported framework, and further apply it to three sets of real DCE-MRI data, before and during the treatment period, for assessing the response to antiangiogenic therapy. The experimental results are not only surprisingly meaningful in biology and clinic, but also capable of reflecting the efficacy of angiogenesis inhibitors in cancer treatment.

Yves Lucet - One of the best experts on this subject based on the ideXlab platform.

  • Techniques and Open Questions in Computational Convex Analysis
    Computational and Analytical Mathematics, 2013
    Co-Authors: Yves Lucet
    Abstract:

    We present several techniques that take advantage of Convexity and use optimal computational geometry algorithms to build fast (log-linear or linear) time algorithms in computational Convex Analysis. The techniques that have strong potential to be reused include: monotonicity of the argmax and injecting Convexity to use that monotonicity, Lipschitzness of the argmin, exploiting various formulas in Convex Analysis, using a graph data structure to vectorize computation, and building a parametrization of the graph. We also point out the potential for parallelization. The techniques can be used as a check list on open problems to find an efficient algorithm. Finally, we list several currently open questions in computational Convex Analysis with links to computational geometry.

  • Fixed-Point Algorithms for Inverse Problems in Science and Engineering - Graph-Matrix Calculus for Computational Convex Analysis
    Springer Optimization and Its Applications, 2011
    Co-Authors: Bryan Gardiner, Yves Lucet
    Abstract:

    We introduce a new family of algorithms for computing fundamental operators arising from Convex Analysis. The new algorithms rely on the fact that the graph of the subdifferential of most Convex operators depends linearly on the graph of the subdifferential of the function. By storing the subdifferential information, the computation of the conjugate is reduced to a matrix multiplication. We explain how other operators can be computed similarly, and present numerical experiments that compare graph-matrix calculus algorithms with piecewise-linear quadratic algorithms from computational Convex Analysis (CCA), and with a bundle method using warmstarting. Our results show that the new algorithms are an order of magnitude faster. They also add subdifferential calculus to our numerical library, and are very simple to implement.

  • Convex Hull Algorithms for Piecewise Linear-Quadratic Functions in Computational Convex Analysis
    Set-valued and Variational Analysis, 2010
    Co-Authors: Bryan Gardiner, Yves Lucet
    Abstract:

    Computing the Convex envelope is a core operation in nonsmooth Analysis that bridges the Convex with the nonConvex world. Although efficient algorithms to compute fundamental transforms of Convex Analysis have been proposed over the years, they are limited to Convex functions until an efficient algorithm becomes available to compute the Convex envelope of a piecewise linear-quadratic function (of one variable) efficiently. We present two such algorithms, one based on maximum and conjugate computation that is easy to implement but has quadratic time complexity, and another based on direct computation that requires more work to implement but has optimal (linear time) complexity. We prove their time (and space) complexity, and compare their performances.

  • What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications
    SIAM Review, 2010
    Co-Authors: Yves Lucet
    Abstract:

    Computational Convex Analysis algorithms have been rediscovered several times in the past by researchers from different fields. To further communications between practitioners, we review the field of computational Convex Analysis, which focuses on the numerical computation of fundamental transforms arising from Convex Analysis. Current models use symbolic, numeric, and hybrid symbolic-numeric algorithms. Our objective is to disseminate widely the most efficient numerical algorithms useful for applications in image processing (computing the distance transform, the generalized distance transform, and mathematical morphology operators), partial differential equations (solving Hamilton-Jacobi equations and using differential equations numerical schemes to compute the Convex envelope), max-plus algebra (computing the equivalent of the fast Fourier transform), multifractal Analysis, etc. The fields of applications include, among others, computer vision, robot navigation, thermodynamics, electrical networks, medical imaging, and network communication.

  • The piecewise linear-quadratic model for computational Convex Analysis
    Computational Optimization and Applications, 2007
    Co-Authors: Yves Lucet, Heinz H. Bauschke, Michael Trienis
    Abstract:

    A new computational framework for computer-aided Convex Analysis is proposed and investigated. Existing computational frameworks are reviewed and their limitations pointed out. The class of piecewise linear-quadratic functions is introduced to improve convergence and stability. A stable Convex calculus is achieved using symbolic-numeric algorithms to compute all fundamental transforms of Convex Analysis. Our main result states the existence of efficient (linear time) algorithms for the class of piecewise linear-quadratic functions. We also recall that such class is closed under Convex transforms. We illustrate the results with numerical examples, and validate numerically the resulting computational framework.

Tsung-han Chan - One of the best experts on this subject based on the ideXlab platform.

  • Convex Analysis based minimum volume enclosing simplex algorithm for hyperspectral unmixing
    International Conference on Acoustics Speech and Signal Processing, 2009
    Co-Authors: Tsung-han Chan, Chong-yung Chi, Yumin Huang
    Abstract:

    Hyperspectral unmixing aims at identifying the hidden spectral signatures (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. Many existing approaches to hyperspectral unmixing rely on the pure-pixel assumption, which may be violated for highly mixed data. A heuristic unmixing criterion without requiring the pure-pixel assumption has been reported by Craig: The endmember estimates are determined by the vertices of a minimum-volume simplex enclosing all the observed pixels. In this paper, using Convex Analysis, we show that the hyperspectral unmixing by Craig's criterion can be formulated as an optimization problem of finding a minimum-volume enclosing simplex (MVES). An algorithm that cyclically solves the MVES problem via linear programs (LPs) is also proposed. Some Monte Carlo simulations are provided to demonstrate the efficacy of the proposed MVES algorithm.

  • WHISPERS - Hyperspectral unmixing from a Convex Analysis and optimization perspective
    2009 First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2009
    Co-Authors: Tsung-han Chan, Chong-yung Chi, A. Arulmurugan
    Abstract:

    In hyperspectral remote sensing, unmixing a data cube into spectral signatures and their corresponding abundance fractions plays a crucial role in analyzing the mineralogical composition of a solid surface. This paper describes a Convex Analysis perspective to (unsupervised) hyperspectral unmixing. Such an endeavor is not only motivated by the recent prevalence of Convex optimization in signal processing, but also by the nature of hyperspectral unmixing (specifically, non-negativity and full additivity of abundances) that makes Convex Analysis a very suitable tool. By the notion of Convex Analysis, we formulate two optimization problems for solving hyperspectral unmixing, which have the intuitive ideas following the works by Craig and Winter respectively but adopt an optimization treatment different from those previous works. We show the connection of the two hyperspectral unmixing optimization problems, by proving that their optimal solutions become identical when pure pixels exist in the data. We also illustrate how the two problems can be conveniently handled by alternating linear programming. Monte Carlo simulations are presented to demonstrate the efficacy of the two hyperspectral unmixing formulations.

  • A Convex Analysis Framework for Blind Separation of Non-Negative Sources
    IEEE Transactions on Signal Processing, 2008
    Co-Authors: Tsung-han Chan, Chong-yung Chi, Yue Wang
    Abstract:

    This paper presents a new framework for blind source separation (BSS) of non-negative source signals. The proposed framework, referred herein to as Convex Analysis of mixtures of non-negative sources (CAMNS), is deterministic requiring no source independence assumption, the entrenched premise in many existing (usually statistical) BSS frameworks. The development is based on a special assumption called local dominance. It is a good assumption for source signals exhibiting sparsity or high contrast, and thus is considered realistic to many real-world problems such as multichannel biomedical imaging. Under local dominance and several standard assumptions, we apply Convex Analysis to establish a new BSS criterion, which states that the source signals can be perfectly identified (in a blind fashion) by finding the extreme points of an observation-constructed polyhedral set. Methods for fulfilling the CAMNS criterion are also derived, using either linear programming or simplex geometry. Simulation results on several data sets are presented to demonstrate the efficacy of the proposed method over several other reported BSS methods.

  • ISBI - Convex Analysis and separation of composite signals in DCE-MRI
    2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008
    Co-Authors: Li Chen, Tsung-han Chan, Chong-yung Chi, Peter L. Choyke, Ge Wang, Yue Wang
    Abstract:

    Dynamic functional imaging promises powerful tools for the visualization and elucidation of important disease- causing biological processes, where the pixels often represent a composite of multiple biomarkers independent of spatial resolution. This study exploits both blind source separation and imagery marker characteristics to develop a hybrid method for the separation of mixed yet correlated biomarker distributions in DCE-MRI. A compartment latent variable model is constructed upon which a novel Convex Analysis framework is proposed to provide a close-form algebraic solution to separating composite markers with non-negativity and well-grounded points. A unique non- negative clustered component Analysis is further developed to explicitly consider both partial volume effect and noise contamination. Experimental results show promising and robust extraction of time activity curves and vascular marker images in agreement with biomedical expectations.

  • Convex Analysis for separation of functional patterns in DCE-MRI: A longitudinal study to antiangiogenic therapy
    2008 IEEE Workshop on Machine Learning for Signal Processing, 2008
    Co-Authors: Tsung-han Chan, Chong-yung Chi, Li Chen, P.l. Choyke, Yue Wang
    Abstract:

    Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can characterize vascular heterogeneity, and has potential utility in assessment of the efficacy of angiogenesis inhibitors in cancer treatment. Due to the heterogeneous nature of tumor microvasculature, the measured signals can be represented as the mixture of the permeability images corresponding to different perfusion rates. We recently reported a hybrid Convex Analysis of mixture framework for unmixing of non-negative yet dependent angiogenic permeability distributions (APDs) and perfusion time activity curves (TACs). In our last work, we presented an underlying theory to infer the concept that the TACs can be identified by finding the lateral edges of an observation-constructed Convex pyramid when the well-grounded points exist for all APDs. For fulfilling this concept, a hybrid method including non-negative clustered component Analysis, Convex Analysis, and least-squares fitting with non-negativity constraints was developed. In this paper, we use computer simulations to validate the performance of our reported framework, and further apply it to three sets of real DCE-MRI data, before and during the treatment period, for assessing the response to antiangiogenic therapy. The experimental results are not only surprisingly meaningful in biology and clinic, but also capable of reflecting the efficacy of angiogenesis inhibitors in cancer treatment.

Chong-yung Chi - One of the best experts on this subject based on the ideXlab platform.

  • Convex Analysis based minimum volume enclosing simplex algorithm for hyperspectral unmixing
    International Conference on Acoustics Speech and Signal Processing, 2009
    Co-Authors: Tsung-han Chan, Chong-yung Chi, Yumin Huang
    Abstract:

    Hyperspectral unmixing aims at identifying the hidden spectral signatures (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. Many existing approaches to hyperspectral unmixing rely on the pure-pixel assumption, which may be violated for highly mixed data. A heuristic unmixing criterion without requiring the pure-pixel assumption has been reported by Craig: The endmember estimates are determined by the vertices of a minimum-volume simplex enclosing all the observed pixels. In this paper, using Convex Analysis, we show that the hyperspectral unmixing by Craig's criterion can be formulated as an optimization problem of finding a minimum-volume enclosing simplex (MVES). An algorithm that cyclically solves the MVES problem via linear programs (LPs) is also proposed. Some Monte Carlo simulations are provided to demonstrate the efficacy of the proposed MVES algorithm.

  • WHISPERS - Hyperspectral unmixing from a Convex Analysis and optimization perspective
    2009 First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2009
    Co-Authors: Tsung-han Chan, Chong-yung Chi, A. Arulmurugan
    Abstract:

    In hyperspectral remote sensing, unmixing a data cube into spectral signatures and their corresponding abundance fractions plays a crucial role in analyzing the mineralogical composition of a solid surface. This paper describes a Convex Analysis perspective to (unsupervised) hyperspectral unmixing. Such an endeavor is not only motivated by the recent prevalence of Convex optimization in signal processing, but also by the nature of hyperspectral unmixing (specifically, non-negativity and full additivity of abundances) that makes Convex Analysis a very suitable tool. By the notion of Convex Analysis, we formulate two optimization problems for solving hyperspectral unmixing, which have the intuitive ideas following the works by Craig and Winter respectively but adopt an optimization treatment different from those previous works. We show the connection of the two hyperspectral unmixing optimization problems, by proving that their optimal solutions become identical when pure pixels exist in the data. We also illustrate how the two problems can be conveniently handled by alternating linear programming. Monte Carlo simulations are presented to demonstrate the efficacy of the two hyperspectral unmixing formulations.

  • A Convex Analysis Framework for Blind Separation of Non-Negative Sources
    IEEE Transactions on Signal Processing, 2008
    Co-Authors: Tsung-han Chan, Chong-yung Chi, Yue Wang
    Abstract:

    This paper presents a new framework for blind source separation (BSS) of non-negative source signals. The proposed framework, referred herein to as Convex Analysis of mixtures of non-negative sources (CAMNS), is deterministic requiring no source independence assumption, the entrenched premise in many existing (usually statistical) BSS frameworks. The development is based on a special assumption called local dominance. It is a good assumption for source signals exhibiting sparsity or high contrast, and thus is considered realistic to many real-world problems such as multichannel biomedical imaging. Under local dominance and several standard assumptions, we apply Convex Analysis to establish a new BSS criterion, which states that the source signals can be perfectly identified (in a blind fashion) by finding the extreme points of an observation-constructed polyhedral set. Methods for fulfilling the CAMNS criterion are also derived, using either linear programming or simplex geometry. Simulation results on several data sets are presented to demonstrate the efficacy of the proposed method over several other reported BSS methods.

  • ISBI - Convex Analysis and separation of composite signals in DCE-MRI
    2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008
    Co-Authors: Li Chen, Tsung-han Chan, Chong-yung Chi, Peter L. Choyke, Ge Wang, Yue Wang
    Abstract:

    Dynamic functional imaging promises powerful tools for the visualization and elucidation of important disease- causing biological processes, where the pixels often represent a composite of multiple biomarkers independent of spatial resolution. This study exploits both blind source separation and imagery marker characteristics to develop a hybrid method for the separation of mixed yet correlated biomarker distributions in DCE-MRI. A compartment latent variable model is constructed upon which a novel Convex Analysis framework is proposed to provide a close-form algebraic solution to separating composite markers with non-negativity and well-grounded points. A unique non- negative clustered component Analysis is further developed to explicitly consider both partial volume effect and noise contamination. Experimental results show promising and robust extraction of time activity curves and vascular marker images in agreement with biomedical expectations.

  • Convex Analysis for separation of functional patterns in DCE-MRI: A longitudinal study to antiangiogenic therapy
    2008 IEEE Workshop on Machine Learning for Signal Processing, 2008
    Co-Authors: Tsung-han Chan, Chong-yung Chi, Li Chen, P.l. Choyke, Yue Wang
    Abstract:

    Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can characterize vascular heterogeneity, and has potential utility in assessment of the efficacy of angiogenesis inhibitors in cancer treatment. Due to the heterogeneous nature of tumor microvasculature, the measured signals can be represented as the mixture of the permeability images corresponding to different perfusion rates. We recently reported a hybrid Convex Analysis of mixture framework for unmixing of non-negative yet dependent angiogenic permeability distributions (APDs) and perfusion time activity curves (TACs). In our last work, we presented an underlying theory to infer the concept that the TACs can be identified by finding the lateral edges of an observation-constructed Convex pyramid when the well-grounded points exist for all APDs. For fulfilling this concept, a hybrid method including non-negative clustered component Analysis, Convex Analysis, and least-squares fitting with non-negativity constraints was developed. In this paper, we use computer simulations to validate the performance of our reported framework, and further apply it to three sets of real DCE-MRI data, before and during the treatment period, for assessing the response to antiangiogenic therapy. The experimental results are not only surprisingly meaningful in biology and clinic, but also capable of reflecting the efficacy of angiogenesis inhibitors in cancer treatment.

Yitan Zhu - One of the best experts on this subject based on the ideXlab platform.

  • Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources.
    Scientific reports, 2016
    Co-Authors: Yitan Zhu, Niya Wang, David J. Miller, Yue Wang
    Abstract:

    Blind Source Separation (BSS) is a powerful tool for analyzing composite data patterns in many areas, such as computational biology. We introduce a novel BSS method, Convex Analysis of Mixtures (CAM), for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the Convex data scatter plot. We propose and prove a sufficient and necessary condition for identifying the mixing matrix through edge detection in the noise-free case, which enables CAM to identify the mixing matrix not only in the exact-determined and over-determined scenarios, but also in the under-determined scenario. We show the optimality of the edge detection strategy, even for cases where source well-groundedness is not strictly satisfied. The CAM algorithm integrates plug-in noise filtering using sector-based clustering, an efficient geometric Convex Analysis scheme, and stability-based model order selection. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data of ovarian cancer subtypes. We apply CAM to dissect dynamic contrast-enhanced magnetic resonance imaging data taken from breast tumors and time-course microarray gene expression data derived from in-vivo muscle regeneration in mice, both producing biologically plausible decomposition results.

  • Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources
    arXiv: Machine Learning, 2014
    Co-Authors: Yitan Zhu, Niya Wang, David J. Miller, Yue Wang
    Abstract:

    Blind Source Separation (BSS) has proven to be a powerful tool for the Analysis of composite patterns in engineering and science. We introduce Convex Analysis of Mixtures (CAM) for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the Convex data scatter plot. We prove a sufficient and necessary condition for identifying the mixing matrix through edge detection, which also serves as the foundation for CAM to be applied not only to the exact-determined and over-determined cases, but also to the under-determined case. We show the optimality of the edge detection strategy, even for cases where source well-groundedness is not strictly satisfied. The CAM algorithm integrates plug-in noise filtering using sector-based clustering, an efficient geometric Convex Analysis scheme, and stability-based model order selection. We demonstrate the principle of CAM on simulated data and numerically mixed natural images. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data. We then apply CAM to dissect dynamic contrast-enhanced magnetic resonance imaging data taken from breast tumors and time-course microarray gene expression data derived from in-vivo muscle regeneration in mice, both producing biologically plausible decomposition results.