# ADVANCED IMAGE PROCESSING METHODS FOR ULTRASONIC NDE RESEARCH C. H. Chen, University of Massachusetts Dartmouth, N.

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3 nonnegativity. Then such partial information is incorporated in an optimal criterion, which is minimized or maximized to find estimates of the f and h. If information on f and h are not available then we have a blind deconvolution problem. Generally speaking, the solution may not be unique and exact deconvolution is impossible as a result of the presence of noise and inherent ill-conditioning nature of the problem. Thus, only an approximate deconvolution can be performed. After the deconvolution process, the resulting image should have much less noise and well preserved edges. We now present the five advanced methods for deconvolution without mathematical details. 1) 2D H-infinity based deconvolution Step 1 Formulate the Local State Space (LSS) model Step 2 2D H-infinity identification Step 3 2D H-infinity filtering, equivalent to solving Riccati equation. Step 4 At each iteration, edges are calculated using the Canny operator and entropy is calculated. The iterative process stops when the decrease in entropy becomes negative. 2) 2D HOS based deconvolution Step 1 Image is modeled as 2D autoregressive process. Both 3 rd order and 4 th order cumulants algorithms are considered. Step 2 Compute 2D cumulants Step 3 Obtain the least square estimator of the blur model Step 4 Perform inverse filtering Step 5 Follow Step 4 in H-infinity algorithm given above. 3) Subspace identification method Step 1 Image is decomposed into the input output matrices that forms MISO system Step 2 Perform the projection of the row space of future outputs and future inputs Step 3 Compute the oblique projection, which is then decomposed using singular value decomposition. The procedure is repeated until a measure of convergence is satisfied. Step 4 Follow Step 4 in H-infinity algorithm given above. 4) The method of using neural networks [6] Step 1 Blur identification based on HOS Step 2 Hopfield neural network is used for image reconstruction. Step 3 Follow Step 4 in H-infinity algorithm given above 5) The method using independent component analysis Step 1 Represent image as a sum of independent components. Step 2 Classify the coefficient associated with each independent component as texture or edge. Step 3 Apply nonlinear operation to the coefficients associated with edges Step 4 Reconstructing the image by setting coefficients with texture as zero. All five methods require post-processing to extract objects from highly blurred C-scan images. The results of the H-infinity method are shown in Fig. 2. The results for the HOS method and for the subspace method are very similar. The goal for image restoration is to find a good image estimate f from the degraded version g. This can be considered as a constrained optimization problem and such optimization can be solved by the Hopfield neural network. The result for the fourth method using neural network is shown in Fig. 3. Both pre-processing and post-processing that involve contrast

4 adjustment are required. Results for the fifth method using independent component are reported elsewhere in this proceedings [8]. Concluding Remarks: All five methods are quite effective as they are theoretically sound. It is difficult to draw definitive conclusion of which one is the best, as this would require much more computer results on different ultrasound C-scan images. All methods perform better than the Wiener filtering as expected with the performance measure of entropy, or mean square error, or ratio of standard deviation to mean. All methods require considerable amount of computation, making it difficult for real-time operation. For three-dimensional image sequence, the computation amount is even more demanding. Further work is needed to improve the implementation of algorithms and to test on additional ultrasonic C-scan images. The potential benefit for ultrasonic NDE research, as well as for medical imaging problems is enormous however. References: 1. R. Gonzalez and R. Woods, Digital Image Processing, Prentice-Hall U. Qidwai and C.H. Chen, 2D H-infinity based blind deconvolution for image enhancement with applications to ultrasonic NDE, IEEE Signal Processing Letters, May U. Qidwai and C.H. Chen, Blind enhancement for ultrasonic C-scans using recursive 2-D H-infinity based state estimation and filtering, INSIGHT- Journal of British Institute of NDT,, vol. 42, no. 11, Nov C.H. Chen and U. Qidwai, Recent trends in 2D blind deconvolution for nondestructive evaluation, Tamkang Journal of Science and Engineering, vol. 5, no. 2, June U. Qidwai and C.H. Chen, C-scan enhancement using recursive subspace deconvolution, in Review of Quantitative Nondestructive Evaluation, vol. 21, AIP, Zhong Wang and C.H. Chen, Ultrasonic image blind deconvolution using higher order statistics and Hopfield neural network, Technical Report ECE (ATMC-NDE-08-01), Univ. of Massachusetts Dartmouth, N. Dartmouth, MA USA 7. C.H. Chen and Xianju Wang, Speckle reduction and edge enhancement of NDE C-scan images using ICA, in Review of Quantitative Nondestructive Evaluation, vol. 23, AIP, C.H. Chen and Xianju Wang, Ultrasonic NDE image enhancement with nonlinear filters in signal subspaces, Proc. of the 16 th WCNDT, Montreal, Canada 2004.

5 (a) (b) Entropy Iterations (c) (d) Figure 2 (a) Sample image, (b) corresponding edges, (c) entropy curve, (d) final image after H-infinity deconvolution. Figure 3 Images after post-processing: original (upper) and neural network (method 4) restoration result (lower), after contrast adjustment.

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