RESTORATION AND PHASE UNWRAPPING OF COMPLEXVALUED IMAGES WITH STOCHASTICS ENERGY MINIMIZATION APPROACH - ADI NIM: 33205011); Tim Pembimbing : Prof. Dr. Ir. Tati Latifah R Mengko; Prof. Andriyan Ba, KUSWORO
A digital image can be modeled as a matrix of picture elements (pixels) of certain intensity. If the pixel intensity is complex-valued, the image can be considered as a complex-valued image. Some examples of complex-valued image are InSAR and MRI image. The nature of magnitude and phase in complex-valued images requires a method which can treat both components consistently, such that loss of information due to the noise effect could be minimized. Methods which address these particular problems in complex-valued images are image restoration and Phase Unwrapping (PU). Phase image reconstruction from its wrapped representation is called PU. A phase reconstruction or Ã‚Â“unwrappingÃ‚Â” aims to recover an absolute phase from its wrapped value by finding the suitable phase cycle which relates the wrapped intensity to its absolute value. PU Algorithms which are known nowadays can be classified into two major categories, i.e. the Local and Global Method. Ideally, without any phase noise, singularity, and/or aliasing, it should be possible to perform phase unwrapping straightforwardly. However, in fact, phase data always contains some disturbances and discontinuity, which add the complexity of PU. In relation to the above-mentioned complexity, we propose a phase reconstruction method which is deliberately based on a stochastic energy minimization approach. An underlying concept of this approach is modeling of the image degradation by noise as a process that increases the energy of a system, such that the image restoration from noise can be modeled as a gradual energy minimization scheme. In this research, a stochastic energy minimization is evaluated for a neighbouring pixels of level 1, level 2, and level 3. The methods calculate the probability of the neighborhood pixels in gaining appropriate phase cycle, which would correspond to a lower energy of the system. This calculation is conducted iteratively until the system energy converges to a minimum. In this condition, the change of energy (ΔE) would be approaching zero (0). The main objective of this research is to produce a method which can improve the performance of restoration and PU by applying a stochastic energy minimization method evaluated on neigbouring pixels. The second objective is to develop frontier methods in image processing. Whereas the benefit of this research is to provide assistance in analysing complex-valued image data which otherwise could have been falsely interpreted in the presence of noise. This research mostly addresses the modeling and computation aspects of image degradation phenomenon in complex-valued images, with the following steps: literary study to map the state-of-the art of related science, adaptation, innovation, and synthesis, computer-based model development, simulations, and testing, model validation on real data, i.e. MRI and InSAR images, and evaluation by comparing the performance of the developed method to the available (published) ones. It is expected that the result produced from this methodology could have a significant effect in the development of science in general, and in the fields of phase image restoration and reconstruction in specifics. The simulation of gray scale image restoration with stochastic energy minimization has been successfully performed in various image sizes. The restoration performance depends solely on the noise level, i.e. the higher the noise level, the lower the recovered PSNR value; with the optimum restoration performance in the noise level of 0 Ã‚Â– 0.6. During this simulation, processing time increases with the increase in image size. The performance evaluation of phase unwrapping with stochastic energy minimization of neighbouring pixels has been successfully conducted as well. The value of recovered PNSR has been influenced by some factors: neigborhood level, coherent, and image type. This algorithm can produce the coherence of 0.8 Ã‚Â– 1 for gaussian surface and inclined image, and 0.4 Ã‚Â– 1 for fBm surface, with the image size of 128 x 128 and 256 x 256. The most stable and effective neigborhood levels are observed in the level 1 and level 3 for all image types. The most effective processing time for this algorithm is obtained in the image size under 512 x 512 with the maximum neigborhood level of 3. This method has potential applications in the field of geology, such as : in the InSAR images to determine the Digital Elevation Map (DEM) and observe geological deformation. Moreover, it can also be applied in the biomedical field, such as : in the MRI images to separate water and fat voxel content, map the distribution of blood flow velocity, and create tissue temperature distribution map for detection of cancer.