Evaluation of Deconvolution Methods for PRISM imagesearth.esa.int/workshops/ALOS2008/participants/253/... · Evaluation of Deconvolution Methods for PRISM Images > Peter Schwind >

1Evaluation of Deconvolution Methods for PRISM images > Peter Schwind > 03.11.2008

Evaluation of Deconvolution Methods for PRISM images

Peter Schwind, Gintautas Palubinskas, Tobias Storch, Rupert MüllerRemote Sensing Technology Inst. (IMF)

German Aerospace Center (DLR)

November 2008, ALOS PI Joint Symposium

Evaluation of Deconvolution Methods for PRISM Images > Peter Schwind > 03.11.2008

2

Outline

IntroductionALOS ProcessorDeconvolution

Deconvolution methodsWiener deconvolutionRichardson-Lucy deconvolutionCOWPATH

Parameter EstimationExperiments and ObservationsConclusions


3

IntroductionALOS Processor

Input processor:

Radiometric corr.:

Geometric corr.:

Atmospheric corr.:

Output processor:


4

IntroductionDeconvolution

Deconvolution of an image i with a point-spread function h is defined as:

where O,I and H are the Fourier transforms of o, i, and h

* =

-1

i * h-1 = o

1),(),(),( −= yxHyxIyxO


5

IntroductionDeconvolution

In practice, this formula cannot be applied due to noise influenceThere are many different deconvolution approaches which differ

mostly in the way they handle the noise amplification (some examples are: wavelet, blind, iterative deconvolution)

We compared three different methods for the deconvolution of PRISM images:

Wiener deconvolutionRichardson-Lucy deconvolution Complex Wavelet Packet Automatic Thresholding(COWPATH)


6

Deconvolution MethodsWiener Deconvolution

Developed by N. Wiener (1949)Wiener deconvolution is one of the most widespread deconvolution algorithmsOptimal tradeoff between inverse filtering and noise smoothingTries to find the deconvolved image with the minimum mean-squared error with the original image

),(

)(1),(

),(),(),(ˆ

2

21 yxI

ISNRyxH

yxHyxHyxO

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+= −


7

Deconvolution MethodsRichardson-Lucy Deconvolution

Developed by W.H.Richardson (1972) and L.B.Lucy (1974)Iterative approachTries to reconstruct the image which, if it is convolved with the PSF again, has the maximum likelihood to again produce the blurred imageOriginal implementation was designed for images with Poisson distributed noiseAn implementation by Pruksch and Fleischmann (1998) modified for Gaussian noise was used

( ) ( )( )[ ] ( )⎥⎦

⎤⎢⎣

⎡=+ yxHyxOyxH

yxHyxIyxOyxOi

ii ,),(ˆ,,,),(ˆ),(ˆ

1


8

Deconvolution MethodsComplex Wavelet Packet Automatic Thresholding

COWPATH was developed by A. Jalobeanu (2000)Based on the working principle of most wavelet based deconvolution algorithms:

Deconvolve the image using a simple inverse filterReduce the noise amplified by the inverse filter by thresholding the coefficients of a wavelet transform

COWPATH makes use of the fact that complex wavelet packets are shift invariant and provide good directional propertiesJalobeanu suggests several variants of the algorithm, which differ mostly in the estimation and application of an efficient threshold


9

Parameter EstimationPoint Spread Function

Since no measurements of the Point Spread Function (PSF) were available they had to be estimated Slanted edge method:

Several profiles of a slanted edge which is assumed to be sharp in the undistorted image are overlaid over each other to obtain theEdge Spread Function (ESF)The ESF is differentiated to obtain the Line Spread Function (LSF)The LSF in X- and in Y-direction is used to construct a horizontally and vertically symmetric PSF


10

Parameter EstimationNoise Standard Deviation

To estimate the noise standard deviation, the standard deviations of several homogeneous areas was measuredTo make sure that the standard deviation does not vary to much over different intensities, the standard deviations of several such areas with various intensities were computedThe average standard deviation of these areas was used as the noise standard deviation


11

ExperimentsApplication to real data

Original Wiener

Richardson-Lucy COWPATH


12

Experiments

To evaluate the deconvolution performance, test images were convolved with a known PSF and Gaussian noise was added to the images.The images were then deconvolved using the known convolution parameters and the deconvolved images were compared to the original images using two metrics:

Signal-to-Noise Ratio (SNR)

Root Mean Squared Error (RMSE)

In addition to that, the turnaround time (TAT) of the algorithms was measured

)ˆ()(log10)ˆ,(ooVar

oVarooSNR−

=

( )wh

ooooRMSE

w

x

h

y yxyx∑ ∑= =−

= 1 12

,, ˆ)ˆ,(


13

ExperimentsSNR


14

ExperimentsRMSE


15

ExperimentsTAT


16

Conclusions

All tested deconvolution methods are able to improve the PRISM image qualityOf the three tested algorithms RL deconvolution showed the best performance (when measured using the SNR or RMSE similarity metrics)An undesirable side-effect of the deconvolution is, that the JPEG artifacts present in PRISM images become even more visible

Maybe an additional JPEG noise reduction step could help to reduce the compression noise


17

Thank you for your attention!

Documents

Evaluation of Deconvolution Methods for PRISM imagesearth.esa.int/workshops/ALOS2008/participants/253/... · Evaluation of Deconvolution Methods for PRISM Images > Peter Schwind >