Introduction:
Shapelets are a complete, orthonormal set of 2D basis functions constructed
from Laguerre or Hermite polynomials weighted by a Gaussian. A linear
combination of these functions can be used to model any image, in a similar way
to Fourier or wavelet synthesis. The shapelet decomposition is particularly
efficient for images localised in space, and provide a high level of
compression for individual galaxies in astronomical data. The basis has many
elegant mathematical properties that make it convenient for image analysis and
processing. The formalism was first introduced to astronomy by Alexandre
Refregier & David Bacon, and a related method has also been independently
suggested by Gary Bernstein & Mike Jarvis.
This shapelets web site is maintained by
Richard Massey.
IDL shapelets software:
The IDL shapelets software requires IDL v5.4 or above.
A standalone set of core routines is available, including
everything you need to decompose images into shapelets and to manipulate them.
Routines to generate multicolour simulated astronomical images are also
now documented and publicly available.
We would be interested to collaborate with anyone requiring more
advanced applications.
Published shapelets papers:
These papers describe the core shapelets method, and define the notation and
conventions used by the publicly available IDL code.
The following papers describe various applications of shapelets. Note that some of these papers use
slightly different notation and conventions. Also try searching for more shapeletsrelated papers on
astroph,
NASA ADS
or google scholar.
 Laguerre 2Dfunctions and their application in quantum optics
Wünsche A. 1998, J. Phys. A: Math. Gen., 31, 8267
 General Hermite and Laguerre twodimensional polynomials
Wünsche A. 2000, J. Phys. A: Math. Gen., 33, 1603
 Image Simulation with Shapelets
Massey R., Refregier A., Conselice C. & Bacon D. 2004, MNRAS 348 214
 Modal decomposition of astronomical images with application to shapelets
Berry R., Hobson M. & Withington S. 2004, MNRAS , 354, 199
 Optical coherence tomography of skin for measurement of epidermal thickness by shapeletbased image analysis
Weissman J., Hancewicz T. & Kaplan P., 2004, Optics Express 12, 23, 5760
 Morphological Classification of Galaxies by Shapelet Decomposition in the SDSS
Kelly B. & McKay T. 2004, AJ, 127, 625
 Morphological Classification of Galaxies by Shapelet Decomposition in the SDSS II: Multiwavelength Classification
Kelly B. & McKay T. 2005, AJ, 129, 1287
 Shapelets correlated with surface normals produce surfaces
Kovesi P., 2005, Computer Vision ICCV 2, 994
 Representation of Sun Spots with Shapelets
Young C., Gallagher P., Ireland J. & McAteer R., 2005, American Geophysical Union SMSP, 11, 7
 Properties and possibilities of quantum shapelets
Coffey M., 2006, JPhysA, 39, 877
 General integrated field spectrograph simulation
Tilquina A., Bonissent A., Aumeunier M., Prieto E., Ealet A., Gerdes D. & Macaire C., 2006 New Astronomy Reviews 50, 4, 275
 Reliable Shapelet Image Analysis
Melchior P., Meneghetti M. & Bartelmann M., 2006, A&A 463, 1215
 GaaP: PSF and aperturematched photometry using shapelets
Kuijken K., 2006, A&A submitted
 Simultaneously band and space limited functions in two dimensions, and receptive fields of visual neurons
Victor J. & Knight B. 2003, Springer Applied Mathematical Sciences Series, p. 375420. Eds: E.Kaplan, J. Marsden, and K. R. Sreenivasan. Springer
 Responses of V1 Neurons to TwoDimensional Hermite Functions
Victor J., Mechler F., Repucci M., Purpura K. & Sharpee T. 2005, J. Neurophysiol 95, 379
 Contextual modulation of V1 receptive fields depends on their spatial symmetry
Sharpee T. & Victor J. 2008, J. Comp. Neuroscience 26, 203
 Laminar and OrientationDependent Characteristics of Spatial Nonlinearities: Implications for the Computational Architecture of Visual Cortex
Victor J., Mechler F., Ohiorhenuan I., Schmid A. & Purpura K. 2009, J. Neurophysiol 102, 3414
The following papers specifically discuss the use of shapelets to measure
weak gravitational lensing.
 Shapelets: II. A Method for Weak Lensing Measurements
Refregier A. & Bacon D. 2003, MNRAS 338 48
 Shapes and Shears, Stars and Smears: Optimal Measurements for Weak Lensing
Bernstein G. & Jarvis M. 2002, AJ, 123, 2
 Shape Reconstruction and Weak Lensing Measurement with Interferometers: A Shapelet Approach
Chang T.C. & Refregier A. 2002, ApJ, 570, 447
 The Galaxy Octopole Moment as a Probe of Weak Lensing Shear Fields
Goldberg D. & Natarajan P. 2002, ApJ, 564, 65
 Optimal Galaxy Shape Measurements for Weak Lensing Applications using the HST ACS
Park Y., Casertano S. & Ferguson H. 2003, ApJ, 600, L159
 Weak Lensing from Space II: Dark Matter Mapping
Massey R., Rhodes J., Refregier A. et al. 2004, AJ, 127, 3089
 Weak Lensing by LargeScale Structure with the FIRST Radio Survey
Chang T.C., Refregier A. & Helfand D., 2004, ApJ, 617, 794
 Extraction of relative magnification matrices from VLBI observations of gravitational lens systems
Bähren L., Schneider P. & King L., 2002, evlb conf. 201
 Observations of cluster substructure using weakly lensed sextupole moments
Irwin J. & Shmakova M. 2003
 GalaxyGalaxy Flexion: Weak Lensing to Second Order
Goldberg D. & Bacon D. 2004, ApJ, 619, 741
 Shapelets "multiple multipole" shear measurement methods
Massey R., Refregier A. & Bacon D., 2005, IAU symp. 225, 31
 Mass modeling of Abell 1689 Advanced Camera for Surveys observations with a perturbed NavarroFrenkWhite model
Zekser K., White R., Broadhurst T., Benítez N., Ford H., Illingworth G., Blakeslee J., Postman M., Jee M. & Coe D., 2006, ApJ, 640, 639
 Shears from shapelets
Kuijken K., 2006, A&A 456, 827
 Weak gravitational shear and flexion with polar shapelets
Massey R., Rowe B., Refregier A., Bacon D. & Berge J., 2007, MNRAS 380, 229
 Measuring Flexion
Goldberg D. & Leonard A., 2007, ApJ 660, 1003
 The Shear TEsting Programme 2: Factors affecting high precision weak lensing analyses
Massey R. et al. 2007, MNRAS 376, 13
Online resources:
Talks:

Shapelets: A New Method to Measure Galaxy Shapes
Refregier, Chang & Bacon 2002. Proceedings of the Workshop
"The Shapes of Galaxies and their Halos", Yale, May 2001

Shapelets "Multiple Multipole" Measurement Method
Massey, Refregier, & Bacon 2004. Proceedings of the Workshop
"Impact of gravitaional lensing on cosmology", Lausanne, July 2004
 Simulated Images with Shapelets
6.4Mb Powerpoint file from
IoA seminar, October 2002
 Shapelets for Shear Surveys
8.3Mb Powerpoint file from
"Structure Evolution and Cosmology", ESO Santiago, October 2002
People: