Evaluation of Deconvolution Methods for PRISM images

Transcription

1 Evaluation of Deconvolution Methods for PRISM images Peter Schwind, Gintautas Palubinskas, Tobias Storch, Rupert Müller Remote Sensing Technology Inst. (IMF) German Aerospace Center (DLR) November 2008, ALOS PI Joint Symposium Evaluation of Deconvolution Methods for PRISM images > Peter Schwind >

2 Outline Introduction ALOS Processor Deconvolution Deconvolution methods Wiener deconvolution Richardson-Lucy deconvolution COWPATH Parameter Estimation Experiments and Observations Conclusions 2

3 Introduction ALOS Processor Input processor: Radiometric corr.: Geometric corr.: Atmospheric corr.: Output processor: 3

4 Introduction Deconvolution Deconvolution of an image i with a point-spread function h is defined as: O( x, y) = I( x, y) H ( x, y) 1 where O,I and H are the Fourier transforms of o, i, and h i * h -1 = o -1 * = 4

5 Introduction Deconvolution In practice, this formula cannot be applied due to noise influence There 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 deconvolution Richardson-Lucy deconvolution Complex Wavelet Packet Automatic Thresholding (COWPATH) 5

6 6 Deconvolution Methods Wiener Deconvolution Developed by N. Wiener (1949) Wiener deconvolution is one of the most widespread deconvolution algorithms Optimal tradeoff between inverse filtering and noise smoothing Tries to find the deconvolved image with the minimum meansquared error with the original image ), ( ) ( 1 ), ( ), ( ), ( ), ˆ( y x I I SNR y x H y x H y x H y x O + =

7 Deconvolution Methods Richardson-Lucy Deconvolution Developed by W.H.Richardson (1972) and L.B.Lucy (1974) Iterative approach Tries to reconstruct the image which, if it is convolved with the PSF again, has the maximum likelihood to again produce the blurred image Original implementation was designed for images with Poisson distributed noise An implementation by Pruksch and Fleischmann (1998) modified for Gaussian noise was used ˆ i+ 1( O x, y) = Oˆ ( x, i y) I( x, y) H ( x, y) ( x, y) Oˆ ( x, y) H [ ] H ( x y) i, 7

8 Deconvolution Methods Complex 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 filter Reduce 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 properties Jalobeanu suggests several variants of the algorithm, which differ mostly in the estimation and application of an efficient threshold 8

9 Parameter Estimation Point 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 the Edge 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 9

10 Parameter Estimation Noise Standard Deviation To estimate the noise standard deviation, the standard deviations of several homogeneous areas was measured To 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 computed The average standard deviation of these areas was used as the noise standard deviation 10

11 Experiments Application to real data Original Wiener Richardson-Lucy COWPATH 11

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) Var( o) SNR( o, oˆ) = 10log Var( o oˆ) Root Mean Squared Error (RMSE) ( ) w h = =, ˆ o o x 1 y 1 x y x, y RMSE( o, oˆ) = wh In addition to that, the turnaround time (TAT) of the algorithms was measured 2 12

13 Experiments SNR 13

14 Experiments RMSE 14

15 Experiments TAT 15

16 Conclusions All tested deconvolution methods are able to improve the PRISM image quality Of 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 16

17 Thank you for your attention! 17