Morphological Component Analysis: An Adaptive Thresholding Strategy

Bobin, J.; Starck, Jean-Luc; Fadili, Jalal M.; Moudden, Y.; Donoho, David L.

doi:10.1109/tip.2007.907073

Cited by 280 publications

(182 citation statements)

References 23 publications

Supporting

Mentioning

182

Contrasting

Order By: Relevance

“…• Empirical work, showing that combined representations such as wavelets with curvelets or wavelets with sinusoids often gave very compelling separations of real signals and images, see, for instance, [1,10,25,26,35,42,40,41,43,44,30,47].…”

Section: Minimum ℓ 1 Decomposition and Perfect Separationmentioning

confidence: 99%

Microlocal Analysis of the Geometric Separation Problem

Donoho

Kutyniok

2012

Comm Pure Appl Math

190

View full text Add to dashboard Cite

Image data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to process a single image and extract two geometrically 'pure' images, each one containing features from only one of the two geometric constituents. This seems to be a seriously underdetermined problem, but recent empirical work achieved highly persuasive separations.We present a theoretical analysis showing that accurate geometric separation of point and curve singularities can be achieved by minimizing the ℓ 1 norm of the representing coefficients in two geometrically complementary frames: wavelets and curvelets. Driving our analysis is a specific property of the ideal (but unachievable) representation where each content type is expanded in the frame best adapted to it. This ideal representation has the property that important coefficients are clustered geometrically in phase space, and that at fine scales, there is very little coherence between a cluster of elements in one frame expansion and individual elements in the complementary frame. We formally introduce notions of cluster coherence and clustered sparsity and use this machinery to show that the underdetermined systems of linear equations can be stably solved by ℓ 1 minimization; microlocal phase space helps organize the calculations that cluster coherence requires.

show abstract

Section: Minimum ℓ 1 Decomposition and Perfect Separationmentioning

confidence: 99%

Microlocal Analysis of the Geometric Separation Problem

Donoho

Kutyniok

2012

Comm Pure Appl Math

190

View full text Add to dashboard Cite

show abstract

“…Noise levels are computed using median absolute deviation (Donoho & Johnstone 1994). Although linear or exponential laws are well suited to such problems (Starck et al 2004), we choose here to rely on a more adaptive strategy based on minimum of maximums (MOM, see Bobin et al 2007).…”

Section: Thresholding Strategymentioning

confidence: 99%

Multi-band morpho-Spectral Component Analysis Deblending Tool (MuSCADeT): Deblending colourful objects

Joseph¹,

Courbin²,

Starck³

2016

A&A

Self Cite

View full text Add to dashboard Cite

We introduce a new algorithm for colour separation and deblending of multi-band astronomical images called MuSCADeT which is based on Morpho-spectral Component Analysis of multi-band images. The MuSCADeT algorithm takes advantage of the sparsity of astronomical objects in morphological dictionaries such as wavelets and their differences in spectral energy distribution (SED) across multi-band observations. This allows us to devise a model independent and automated approach to separate objects with different colours. We show with simulations that we are able to separate highly blended objects and that our algorithm is robust against SED variations of objects across the field of view. To confront our algorithm with real data, we use HST images of the strong lensing galaxy cluster MACS J1149+2223 and we show that MuSCADeT performs better than traditional profile-fitting techniques in deblending the foreground lensing galaxies from background lensed galaxies. Although the main driver for our work is the deblending of strong gravitational lenses, our method is fit to be used for any purpose related to deblending of objects in astronomical images. An example of such an application is the separation of the red and blue stellar populations of a spiral galaxy in the galaxy cluster Abell 2744. We provide a python package along with all simulations and routines used in this paper to contribute to reproducible research efforts.

show abstract

“…To evaluate the performance of the method at each iteration we use the adaptive MCA -Mean of Maxima (MCA-MOM) described in [19]. This method yields better performance when the components provide a different directional analysis, and ensures that each transform gets at least one assigned component [17].…”

Section: Mca With Polarimetric Data Setsmentioning

confidence: 99%

Fully polarimetric high-resolution airborne SAR image change detection with morphological component analysis

Domínguez¹,

Henke²,

Small³

et al. 2015

SPIE Proceedings

View full text Add to dashboard Cite

Change detection for high resolution Synthetic Aperture Radar (SAR) imagery requires advanced denoising mechanisms to preserve details and minimize speckle. In this work, we propose a change detector based on a Morphological Component Analysis (MCA) of the scattering mechanisms provided with fully polarimetric data sets. With MCA, the power of each scattering mechanism is decomposed into diverse image features. By introducing a priori knowledge of the content of the scenes, and exploiting both the scattering mechanisms and their corresponding shapes, we can significantly improve performance, with fewer false alarms introduced by clutter, focusing errors, and inconsistent acquisition geometries. ABSTRACTChange detection for high resolution Synthetic Aperture Radar (SAR) imagery requires advanced denoising mechanisms to preserve details and minimize speckle. In this work, we propose a change detector based on a Morphological Component Analysis (MCA) of the scattering mechanisms provided with fully polarimetric data sets. With MCA, the power of each scattering mechanism is decomposed into diverse image features. By introducing a priori knowledge of the content of the scenes, and exploiting both the scattering mechanisms and their corresponding shapes, we can significantly improve performance, with fewer false alarms introduced by clutter, focusing errors, and inconsistent acquisition geometries.

show abstract

Morphological Component Analysis: An Adaptive Thresholding Strategy

Cited by 280 publications

References 23 publications

Microlocal Analysis of the Geometric Separation Problem

Microlocal Analysis of the Geometric Separation Problem

Multi-band morpho-Spectral Component Analysis Deblending Tool (MuSCADeT): Deblending colourful objects

Fully polarimetric high-resolution airborne SAR image change detection with morphological component analysis

Contact Info

Product

Resources

About