Image Deblurring : Comparing the Performance of Analytical and Learning Methods

Blurring is a common phenomenon during image formation due to various factors like motion between the camera and the object, or atmospheric turbulence, or when the camera fails to have the object in focus, which leads to degradation in the image formation process. This leads to the pixels interacting with the neighboring ones, and the captured image is blurry as a result. This interaction with the neighboring pixels, is the 'spread' which is represented by the Point Spread Function. Image deblurring has many applications, for example in Astronomy, medical imaging, where extracting the exact image required might not be possible due to various limiting factors, and what we get is a deformed image. In such cases, it is necessary to use an apt deblurring algorithm keeping all necessary factors like performance and time in mind. This thesis analyzes the performance of learning and analytical methods in Image deblurring Algorithm. Inverse problems would be discussed at first, and how ill posed inverse problems like image deblurring cannot be tackled by naive deconvolution. This is followed by looking at the need for regularization, and how it is necessary to control the fluctuations resulting from extreme sensitivity to noise. The Image reconstruction problem has the form of a convex variational problem, and its prior knowledge acting as the inequality constraints which creates a feasible region for the optimal solution. Interior point methods iterates over and over within this feasible region. This thesis uses the iRestNet Method, which uses the Forward Backward iterative approach for the Machine learning algorithm, and Total Variation approach implemented using the FlexBox tool for analytical method, which uses the Primal Dual approach. The performance is measured using SSIM indices for a range of kernels, the SSIM map is also analyzed for comparing the deblurring efficiency

A Variational Model for Joint Motion Estimation and Image Reconstruction

The aim of this paper is to derive and analyze a variational model for the joint estimation of motion and reconstruction of image sequences, which is based on a time-continuous Eulerian motion model. The model can be set up in terms of the continuity equation or the brightness constancy equation. The analysis in this paper focuses on the latter for robust motion estimation on sequences of twodimensional images. We rigorously prove the existence of a minimizer in a suitable function space setting. Moreover, we discuss the numerical solution of the model based on primal-dual algorithms and investigate several examples. Finally, the benefits of our model compared to existing techniques, such as sequential image reconstruction and motion estimation, are shown.The work of the first author was also supported by the German Science Foundation DFG via EXC 1003 Cells in Motion Cluster of Excellence, M¨unster, German

Ultrasound tomography using pyroelectric and piezoelectric sensors

Acoustic absorption is one of several quantities which can differentiate healthy breast tissue from cancerous tissue. In order to accurately quantify the acoustic absorption, the sensor system must be able to accurately distinguish acoustic power loss due to absorption from other modes of attenuation. Traditional piezoelectric sensors are susceptible to phase-cancellation artifacts due to their directional signal response, and thus pyroelectric ultrasound sensors, which have a much flatter directional response, have been suggested as an alternate measurement device for improved absorption reconstructions in ultrasound tomography (UST). In this thesis we investigate the use of pyroelectric phase-insensitive sensors in UST — the thesis is divided into two parts. In the first part we present a model for a pyroelectric ultrasound sensor and investigate its directional response and sensitivity properties. The model’s time-series response and directional response are compared to real-world measurements to confirm accuracy. The second part focuses on the inverse problem aspect of ultrasound tomography, where we consider various reconstruction methods and sensor geometries to determine which situations can benefit from phase-insensitive data for acoustic absorption reconstruction. Reconstructions for both phase-insensitive as well as phase-sensitive sensors are analysed, with future work considerations for combined sensor systems