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M.Tech (Research) Thesis Defense: “Development of advanced regularization methods to improve photoacoustic tomography”
23 Jan @ 10:30 AM -- 11:30 AM
M.Tech (Research) Thesis Defense
Name of the Student : Dween Rabius Sanny
S.R. Number : 06-18-01-10-22-16-1-14194
Title : Development of advanced regularization methods to improve photoacoustic tomography
Date & Time : 23 January 2019 (Wednesday), 10:30 AM
Venue : CDS Seminar hall #102
Photoacoustic tomography (PAT) has the ability to provide optical contrast at ultrasonic resolution deep inside biological tissue. PAT uses a nanosecond laser pulse to irradiate the tissue under investigation, the transient light is absorbed by different tissue chromophores, resulting in a small rise in temperature in the tissue. The temperature rise generates a pressure wave (also called as photoacoustic waves) due to thermoelastic expansion. The generated PA waves will propagate through the tissue and is measured using broadband ultrasound transducers placed outside the biological tissues. These acoustic measurements are used to estimate the initial pressure rise inside the tissue by solving an acoustic inverse problem. The inversion can be performed by using analytical and model-based methods. The reconstruction schemes like backprojection, filter backprojection, time reversal, delay and sum, or Fourier-based inversion have shown potential in providing qualitative reconstructions with an advantage of having lower computational complexity, but fails in irregular geometries and limited data scenarios.
Model based reconstruction involves inverting a model-matrix that is generated either using impulse response or discretizing the solution of wave equation. Inversion in limited data scenarios is difficult due to ill-conditioned nature of the problem. Therefore typically prior statistics about the image is applied in form of regularization during the inversion. The prior works have attempted to choose the regularization in an automated fashion by minimizing some error metric like residual. In contrary, other schemes were proposed to mitigate the effects of regularization by using deconvolution approach using model-resolution matrix.
Another perspective of regularization lies in its ability to define the resolution characteristic in the imaging domain. The resolution characteristics are heavily influenced by factors like ultrasound transducer sensitivity field, depth dependent fluence, bandwidth of the detector, and detector position etc. This thesis work attempts to develop advanced regularization methods that were based on numerical models as well as semi-norm of the data-fidelity terms.
The first half of thesis attempts to use the concept of model based regularization, which is spatially dependent, to mitigate the non-uniform resolution effects arising in photoacoustic imaging. The hypothesis is that the non-uniform resolution in the imaging domain can be captured using model-resolution. Two regularization schemes within the standard Tikhonov regularization framework, which use model (system matrix) characteristics is proposed here. The first one is fidelity embedded regularization (FER), based on the correlation between the columns of the model matrix, which was proven to be effective in solving inverse problem in Electrical Impedance Tomography. The second regularization scheme is based on model-resolution matrix, which provides the spatially variant characteristics of the model, that is proven to provide superior results compared to other regularization schemes in diffuse optical tomography.
The second half of this thesis work is based on singular value decomposition (SVD) which is widely used in regularization methods to know filtering applied to its spectral (eigen) values of the system. Spectral filtering methods provide improved insight to the problem. Even the standard method (such as Tikhonov regularization) or recently proposed exponential filtering method was formulated within the filtering of singular values of photoacoustic imaging system matrix. The Tikhonov filtering promotes smooth solutions due to the ℓ2-norm regularization. In this work, a fractional Tikhonov filtering was introduced which utilizes the semi-norm in the residual error of the Tikhonov regularization (applied via a weighting matrix given in fractional power), and the fractional power controls the amount of damping or smoothness of the reconstructed photoacoustic images. This method was proven earlier to be effective for solving linear discrete ill-posed problem. Morozov discrepancy principle is a acknowledged method to determine the regularization parameter. The same is effectively deployed via an optimization procedure that uses the simplex method to find the optimal regularization parameter and the fractional power. A mathematical framework was developed to demonstrate the fractional power ability to control the amount of damping or smoothness in the reconstructed solution given different noise scenarios in photoacoustic imaging. By using both digital phantoms and experimental data, it was shown that the proposed fractional Tikhonov method was more robust to noise and provides better performance in terms of standard figures of merit compared to standard Tikhonov and exponential filtering methods.
ALL ARE WELCOME