Image noise reduction by means of regularization methods – Part I

In practical applications of vision systems to mechanical systems vibration measurements, the problem of image reconstruction on the basis of registered noisy image is frequently encountered [6]. Such problem is an inverse, ill-posed problem, which means that even small disturbances of the registered image have significant in fluence on the accuracy of its reconstruction. For the purposes of image noise reduction, regularization methods were used. In the current paper (part I), noise reduction of the test image was carried out by means of the algorithm requiring decomposing matrix modelling noise into singular values, which, in case of images of significant dimensions, requires significant computational effort. Therefore, for the purposes of regularization of images of significant dimensions, in the second paper (part II) the iterative approximate method formulated by the author was used. Obtained results proved that formulated and implemented methods find application to noise reduction of images, the reconstruction of which is impossible to carry out by means of other methods because of the excessive loss of information resulting from imposed noise.

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Praca dotyczy zagadnienia redukcji szumów pomiarowych obrazów z zastosowaniem metody regularyzacji Tichonowa, TSVD, DSVD oraz ME. Rekonstrukcję obrazów przeprowadzono z zastosowaniem sformułowanych i zaimplementowanych przez autorkę algorytmów. Wykazano przydatność sformułowanych metod w przypadku obrazów, których rekonstrukcja nie jest możliwa do przeprowadzenia innymi metodami ze względu na zbyt dużą utratę informacji spowodowaną nałożeniem szumów.