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Correction of phase image background in the digital holographic microscope using convolution
Rudolfová, Zdena ; Malina, Radomír (referee) ; Uhlířová, Hana (advisor)
This bachelor thesis concentrates on a correction of background in the phase image of cells from a transmitted-light digital holographic microscope (TDHM). Optical aberrations in the optical systems of the object and reference arms cause "deformation" of the phase image. The cell is not displayed on a background with a constant value of phase, it is displayed on a background with phase values continuously changing between different places in the image. A method for removing the consequence of this imperfection from the image is described in this thesis. The principle lies in partial convolution of the phase image with a convolution kernel determined by a two-dimensional Gaussian function with the same variance in the both axes. To eliminate loss of information about the cells, the convolution is computed only from those parts of the phase image which contain no cells. The result of the convolution is considered to be an approximation of the background. This approximation is then subtracted from the phase image. The resulting phase image has a constant background, containing only noise. The necessary mathematical concepts are resumed in the introductory part of the thesis. The basic principle of the TDHM image reconstruction is also described. As a part of the thesis, a computer programme Odečet pozadí (Background subtraction) was created, which processes the phase images from the TDHM using this method.
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Convolution Model of Time-activity Curves in Blind Source Separation
Tichý, Ondřej ; Šmídl, Václav
Availability of input and organ functions is a prerequisite for analysis of dynamic image sequences in scintigraphy and positron emission tomography (PET) via kinetic models. In PET, the input function can be directly measured by sampling the arterial blood. This invasive procedure can be substituted by extraction of the input function from the observed images. Standard procedure for the extraction is based on manual selection of a region of interest (ROI) which is user-dependent and inaccurate. The aim of our contribution is to demonstrate a new procedure for simultaneous estimation of the input and organ functions from the observed image sequence. We design a mathematical model that integrates all common assumption of the domain, including convolution of the input function and tissue-specific kernels. The input function as well as the kernel parameters are considered to be unknown. They are estimated from the observed images using the Variational Bayes method.
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Model Consideration for Blind Source Separation of Medical Image Sequences
Tichý, Ondřej
The problem of functional analysis of medical image sequences is studied. The obtained images are assumed to be a superposition of images of underlying biological organs. This is commonly modeled as a Factor Analysis (FA) model. However, this model alone allows for biologically impossible solutions. Therefore, we seek additional biologically motivated assumptions that can be incorporated into the model to yield better solutions. In this paper, we review additional assumptions such as convolution of time activity, regions of interest selection, and noise analysis. All these assumptions can be incorporated into the FA model and their parameters estimated by the Variation Bayes estimation procedure. We compare these assumptions and discuss their influence on the resulting decomposition from diagnostic point of view. The algorithms are tested and demonstrated on real data from renal scintigraphy; however, the methodology can be used in any other imaging modality.
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