Unit:
Κατεύθυνση / ειδίκευση Επεξεργασία-Μάθηση Σήματος και Πληροφορίας (ΕΜΠ)Πληροφορική
Author:
Markoutis Vasilios
Supervisors info:
Σέργιος Θεοδωρίδης Καθηγητής Τμήματος Πληροφορικής και Τηλεπικοινωνιών ΕΚΠΑ
Original Title:
Αποθορυβοποίηση εικόνας μέσω του αλγορίθμου k-SVD
Translated title:
Image denoising with k-SVD algorithm
Summary:
Machine learning algorithms can effectively apply on signal processing problems in a scientific area with wide research interest. One of the big data challenges is to represent large sets of data with mathematical functions consisted of a few variables. Viewing the geometric aspects of the problem, the goal is the representation of data from a higher to a lower subspace without the loss of a large amount of information. This procedure is called dimensionality reduction and it is a difficult problem.
Surprisingly, nature's laws tend to fit well on the big data processing. Nature rejects every unecessary element expressing with this way its parsimony. In mathematical and information science world, this minimalism of nature corresponds to the concept of sparsity. The representation of large sets of data with sparse models reveals relationships between the elements of data and confirms that data on these sets are not randomly distributed.
The remarkable in sparse models, is that sparse representations can reject the useless data defined as noise. Noise is present in every real life problem. The detection and rejection of noise refers to an inverse problem which is infeasible to be solved precisely. However, suitable algorithms using sparse models can reject a large amount of noise on a set of data.
On the other hand, machine learning consists of algorithms which can train a system in order to execute specific procedures depending on the parameters of the problem. From this point of view, sparse representations of a large set of data can be more effective if the dictionary which is used for the sparse model can be resulted from the existing data after the appliance of machine learning algorithms. This technique is called dictionary learning and has introduced modern aspects to the solutions of inverse problems.
In the work at hand, the k-SVD algorithm, which is one of the most famous dictionary learning algorithms, is studied in image denoising problems for different kinds of noise. The k-SVD algorithm in combination with sparse representations algorithms can achieve quite competitive results in image denoising. Digital images are only used for the visualization of the results. Consequently, these algorithms can be used and in other types of signals by the appropriate choice of parameters.
Main subject category:
Technology - Computer science
Keywords:
image processing, overcomplete dictionaries, denoising, machine learning, sparsity, matrix decomposition
