In the field of biomedical imaging, images often report a combination of biologically induced variation, usually the goal of the imaging process (e.g. outlining an anatomical region or disease pattern), and non-biological variation, such as instrument or acquisition method-induced noise patterns.
Since some medical decisions are made based on imaging, separating the biological signal from noise is of significant importance (e.g. accelerates decision-making, reducing the chance of misdiagnosis).
Some non-biological variations that span a wide range of imaging modalities include e.g. viewport stitching artifacts, slice-to-slice interference, aliasing, and Gibbs-phenomena.
From a signal processing perspective, many of these can be modeled as quasiperiodic patterns.
Thus, removal of quasiperiodic patterns while preserving the underlying medical information is the main focus of this thesis.

Although in modern instruments, many forms of non-biological variation can be attenuated to be invisible to the naked eye, machine learning algorithms which are often used for classification of disease and segmentation of biological samples may be susceptible to even minor variations and noise patterns.
Development of entirely data-driven, unsupervised denoising techniques can potentially increase the effectiveness and reliability of such algorithms.
Furthermore, under certain image transformations, such as different color spaces, the Fourier and wavelet transform, and factorizations, such as principal component analysis and non-negative matrix factorization, as well as combinations of these, non-biological patterns can get amplified and become so prominent that much of the underlying biological information is concealed.
Removing these quasiperiodic patterns using current state-of-the-art algorithms still requires manual parameter tuning and prior expert knowledge, which is an impractical and possibly unnecessary expectation towards healthcare professionals.
The goal of this M.Sc. thesis is to develop an automated, data-driven framework, that is able to reliably identify, quantify, and eliminate quasiperiodic patterns within the images while retaining as much biological information as possible.

In this framework, named Quasiperiodic Image Denoising (QID), two novel algorithms are implemented, both operating in the Fourier domain.
One algorithm is based on robust principal component analysis (QID-RPCA) and the other uses the normalized median of absolute differences (QID-MADN).
The methods used to achieve unsupervised, data-driven denoising are described in detail.
This includes the use of histogram equalization for radial binning, an automated, sparsity-based approach to choosing the optimal aggregation level, and noise component attenuation based on radial frequency patterns.
The methodology is demonstrated through three case studies.
First, a synthetic dataset is used to compare the performance of the novel algorithms to the current state-of-the-art solutions.
Second, the performance is evaluated on two real-world datasets processed using a number of methods, e.g. factorization and different color spaces. One of these datasets is based on a microscopy image of a transversal section of a mouse brain and the other one is based on a microscopy image of a coronal section of a rat kidney.
Finally, a real-world, raw dataset is denoised consisting of a set of high-resolution fluorescent microscopy images of a human kidney.
Results indicate that the novel algorithms have higher denoising performance than previous approaches in the literature with notable improvements achieved for low-frequency corruptions.