Electronics And Communications Engineering Nalla Malla Reddy Engineering College Major Project Seminar on “Phase Preserving Denoising of Images” Guide Mrs. T Rajini Assoc. Prof, ECE By A Sravani (08B61A0401) B Naveen Reddy (08B61A0412) Deekshith Allamaneni (08B61A0421)

Contents IntroductionSteps In Phase PreservingLocal Feature ExtractionThresholdingReconstructionConclusionReferences

Introduction Image denoising is a process of recovering the image by eliminating noise which is usually an aspect of electronic noise. Phase information is of crucial importance to human visual perception Figure 1. When phase information from one image is combined with magnitude information of another it is phase information that prevails.

Steps In Phase Preserving Denoising 1. Extract the local phase and amplitude information at each point in the image by applying (a discrete implementation of) the continuous wavelet transform. 2. Determining a noise threshold at each scale and shrinking the magnitudes of the filter response vectors appropriately, while leaving the phase unchanged. 3. Step 1 and 2 are repeated for the set of all scales and rotations (filter bank) of the mother Gabor filter. 4. Reconstruction is achieved by overlapping of transfer functions of all the filters in the filter bank, so that their sum results in an even coverage of the spectrum.

Gabor Filter Frequency and orientation representations of Gabor filters are similar to those of the human visual system. Gaussian Filter’s impulse response is a harmonic function multiplied by a Gaussian function. It is useful for feature extraction and edge detection.

Figure 3. An array of filter response vectors at a point in a signal can be represented as a series of vectors radiating out from the frequency axis. The amplitude specifies the length of each vector and the phase specifies its angle. Note that wavelet filters are scaled geometrically, hence their centre frequencies vary accordingly.

Figure 4. An example of the real part of Gabor wavelets with 4 scales and 8 orientations.

Thresholding Automatically determine the appropriate wavelet shrinkage thresholds. The threshold levels are determined from the statistics of the amplitude responses of the smallest scale filter pair over the image.

Reconstruction Figure 5. (a) Original image. (b), (c), (f), (e) Responses of Gabor filters with different rotations. (d) Reconstructed image.

Conclusion We have presented a denoising algorithm, which recovers the image with a better quality by preserving the perceptually important phase information.

References 1.A. V. Oppenheim and J. S. Lim. The importance of phase in signals. In Proceedings of The IEEE 69, pages 529–541, P. D. Kovesi. Invariant Measures of Image Features From Phase Information. PhD thesis, The University of Western Australia, May Digital Image processing – R.C. Gonzalez & R.E. Woods, Addison Wesley/ Pearson education, 2nd Education, 2002.