Results 1 - 10
of
14
Rank related properties for basis pursuit and total variation regularization
, 2006
"... This paper focuses on optimization problems containing an l 1 kind of regularity criterion and a smooth data fidelity term. A general theorem is applied in this context; it gives an estimate of the distribution law of the “rank ” of the solution to optimization problems, when the initial datum follo ..."
Abstract
-
Cited by 8 (6 self)
- Add to MetaCart
(Show Context)
This paper focuses on optimization problems containing an l 1 kind of regularity criterion and a smooth data fidelity term. A general theorem is applied in this context; it gives an estimate of the distribution law of the “rank ” of the solution to optimization problems, when the initial datum follows a uniform (in a convex compact set) distribution law. It says that, asymptotically, solutions with a large rank are more and more likely. The main goal of this paper is to understand the meaning of this notion of rank for some energies which are commonly used in image processing. We study in detail the energy whose level sets are defined as the convex hull of a finite subset of R N (c.f. Basis Pursuit) and the total variation. For these energies, the notion of rank relates respectively to sparse representation and staircasing. In all cases but the 2D total variation, we are able to adapt the general theorem mentioned above to the energies under consideration. Key words: basis pursuit, sparse representation, total variation, regularization, polytopes
Image processing techniques for assessing contractility in isolated adult cardiac myocytes
- Article ID 352954
"... We describe a computational framework for the comprehensive assessment of contractile responses of enzymatically dissociated adult cardiac myocytes. The proposed methodology comprises the following stages: digital video recording of the contracting cell, edge preserving total variation-based image ..."
Abstract
-
Cited by 2 (2 self)
- Add to MetaCart
We describe a computational framework for the comprehensive assessment of contractile responses of enzymatically dissociated adult cardiac myocytes. The proposed methodology comprises the following stages: digital video recording of the contracting cell, edge preserving total variation-based image smoothing, segmentation of the smoothed images, contour extraction from the segmented images, shape representation by Fourier descriptors, and contractility assessment. The different stages are variants of mathematically sound and computationally robust algorithms very well established in the image processing community. The physiologic application of the methodology is evaluated by assessing overall contraction in enzymatically dissociated adult rat cardiocytes. Our results demonstrate the effectiveness of the proposed approach in characterizing the true, two-dimensional, "shortening" in the contraction process of adult cardiocytes. We compare the performance of the proposed method to that of a popular edge detection system in the literature. The proposed method not only provides a more comprehensive assessment of the myocyte contraction process but also can potentially eliminate historical concerns and sources of errors caused by myocyte rotation or translation during contraction. Furthermore, the versatility of the image processing techniques makes the method suitable for determining myocyte shortening in cells that usually bend or move during contraction. The proposed method can be utilized to evaluate changes in contractile behavior resulting from drug intervention, disease modeling, transgeneity, or other common applications to mammalian cardiocytes.
Extensions in spaces with variable exponents — the half space
- Proceedings of the RIMS meeting on Harmonic Analysis and Nonlinear Partial Differential Equations
"... Abstract. In this article we study the Hardy–Littlewood max-imal operator in variable exponent spaces. For a given variable exponent p on a domain Ω for which the maximal operator is con-tinuous on Lp(·)(Ω) we construct an extension of p to Rn such that the maximal operator is continuous on Rn. The ..."
Abstract
-
Cited by 1 (1 self)
- Add to MetaCart
(Show Context)
Abstract. In this article we study the Hardy–Littlewood max-imal operator in variable exponent spaces. For a given variable exponent p on a domain Ω for which the maximal operator is con-tinuous on Lp(·)(Ω) we construct an extension of p to Rn such that the maximal operator is continuous on Rn. The variable exponent will be constructed by means of a Whitney type extension. In this paper we restrict ourselves to the case where Ω is the half space. But the technique applies to less regular domains. The application to ε-δ-domains (Jones domains) is the subject of a forthcoming article. 1.
rE
"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
Abstract
- Add to MetaCart
(Show Context)
All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
doi:10.1155/2009/352954 Research Article Image Processing Techniques for Assessing Contractility in Isolated Adult Cardiac Myocytes
"... We describe a computational framework for the comprehensive assessment of contractile responses of enzymatically dissociated adult cardiac myocytes. The proposed methodology comprises the following stages: digital video recording of the contracting cell, edge preserving total variation-based image s ..."
Abstract
- Add to MetaCart
We describe a computational framework for the comprehensive assessment of contractile responses of enzymatically dissociated adult cardiac myocytes. The proposed methodology comprises the following stages: digital video recording of the contracting cell, edge preserving total variation-based image smoothing, segmentation of the smoothed images, contour extraction from the segmented images, shape representation by Fourier descriptors, and contractility assessment. The different stages are variants of mathematically sound and computationally robust algorithms very well established in the image processing community. The physiologic application of the methodology is evaluated by assessing overall contraction in enzymatically dissociated adult rat cardiocytes. Our results demonstrate the effectiveness of the proposed approach in characterizing the true, two-dimensional, “shortening ” in the contraction process of adult cardiocytes. We compare the performance of the proposed method to that of a popular edge detection system in the literature. The proposed method not only provides a more comprehensive assessment of the myocyte contraction process but also can potentially eliminate historical concerns and sources of errors caused by myocyte rotation or translation during contraction. Furthermore, the versatility of the image processing techniques makes the method suitable for determining myocyte shortening in cells that usually bend or move during contraction. The proposed method can be utilized to evaluate changes in contractile behavior resulting from drug intervention, disease modeling, transgeneity, or other
Blowup solutions and their blowup rates for parabolic equations with non-standard growth conditions
"... Abstract. This paper concerns classical solutions for homogeneous Dirichlet problem of parabolic equations coupled via exponential sources involving variable exponents. We first establish blowup criteria for positive solutions. And then, for radial solutions, we obtain optimal classification for sim ..."
Abstract
- Add to MetaCart
(Show Context)
Abstract. This paper concerns classical solutions for homogeneous Dirichlet problem of parabolic equations coupled via exponential sources involving variable exponents. We first establish blowup criteria for positive solutions. And then, for radial solutions, we obtain optimal classification for simultaneous and non-simultaneous blowup, which is represented by using the maxima of the involved variable exponents. At last, all kinds of blowup rates are determined for both simultaneous and non-simultaneous blowup solutions.
local compromise between total variation
, 2007
"... Graduated adaptive image denoising: ..."
(Show Context)
