General 1D Reconstruction from Irregular Samples with Variable Apertures: Software Prof. David G. Long Brigham Young University Center for Remote Sensing Microwave Earth Remote Sensing (MERS) Laboratory 459 Clyde Building, Provo, Utah USA long@ee.byu.edu

Software to accompany the paper:
 
D.G. Long and R.O.W. Franz, Band-Limited Signal Reconstruction from Irregular Samples with Variable Apertures, IEEE Transactions on Geoscience and Remote Sensing, to appear, doi:10.1109/TGARS.215.2501366, 2016.

Basic Theory (544kB PDF file)

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General Implemenation one-dimensional reconstruction:

Implements one-dimensional irregularly-spaced samples with (possible) variable apertures using the approach described in Long and Franz (2016) implemented both as described in the paper and in a more efficient fequency-domain way. Includes both no-aperture and variable aperture reconstruction in the same routine. Includes a modified version of the ACT algorighm described in (Feichtinger et al., 1995). The routine demo_recon.m compares each of the different reconstruction methods used in recon.m

References

Feichtinger, H.G., K. Gröchenig, and T. Strohmer, 1995. Efficient numerical methods in non-uniform sampling theory, Numerische Mathematick, vol. 29, pp. 433-440, 1995.

Long, D.G., and R.O.W. Franz, 2016. Band-Limited Signal Reconstruction from Irregular Samples with Variable Apertures, IEEE Transactions on Geoscience and Remote Sensing, to appear, doi:10.1109/TGARS.215.2501366, 2016.

BYU Software copyright 2015 by D.G. Long at BYU. All rights retained. Users may use and modify this software so long as the source paper above is cited. No warrantee of any kind is provided. Note: this code is designed to illustrate the method. No claims are made for its efficiency. ACT algorithm code is based on(Feichtinger et al., 1995) but has been slightly modified to improve its numerical accuracy.

File listing/ (some of these routines are contained on other pages)
README.txt
 
demo_recon.m demonstrates general 1d sampling and reconstruction using recon.m Calls ATC_byu.m, irregrecon.m, and irregreconAp.m as needed.
 
ACT_byu.m a modified version of FGH's ACT algorithm
 
recon.m general discrete 1d irregular reconstruction with or without variable aperatures. Different methods are provided for no-aperture, fixed-aperture, and variable aperture to improved efficiency.
 
irregrecon.m Long and Franz 1d reconstruction w/o aperature
 
irregreconAp.m Long and Franz 1d reconstruction w/variable aperatures
 
Dm.m compute 1d M-order Dirichlet function
 
ApDm.m compute 1d aperture-filtered M-order Dirichlet function
 
randsample1d.m 1d sampling routine used by demo_*.m Can do regular or uniformly-distributed irregular sampling.
 
myfigure.m Matlab utility to replace standard figure call to simplify handing of figures (calls to myfigure in demo*.m can be replaced with calls to matlab's standard "figure" command if the user does not wish to use myfigure.m)
 

Basic Theory (pdf file)

Reconstruction Home