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Two-Dimensional Z-space Filtering Using Pulse-Transfer Function

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Abstract

The main concept of this research is the well-accepted and recognized equation that models the pulse-transfer function (PTF) as the ratio between the Z-transform of the filter output and the Z-transform of the filter input. The proof of concept has been tested to verify the main modelling aspect using theoretical images. The proof of concept is then mathematically extended, so as to use the PTF to filter images in Z-space using Bessel, Butterworth, and type I Chebyshev filters. Z-space filtering is determined using inverse Z-transform of the pointwise multiplication between Z-space of PTF and Z-space of departing image. The filtered image is reconstructed using inverse Z-transform of the Z-space multiplication. Further, the PTF is calculated using scaled data and is called normalized transfer function (NTF). The NTF is then compared to Fourier convolution image. This paper documents methodology and technology used for the calculation of the PTF of discrete digital filters. The proof of concept is verified successfully. The novelty of this research is Z-space filtering in two dimensions using PTF.

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Data availability

The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Software is freely available to the public upon request.

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Acknowledgements

The author expresses sincere gratitude for the MR images provided by Dr. Dimitar Veljanovski and Dr. Filip A. Risteski. The author is also very grateful to Professor Ustijana Rechkoska Shikoska because of the coordination of the human resources. Dr. Dimitar Veljanovski and Dr. Filip A. Risteski are affiliated with the Department of Radiology at the General Hospital 8-mi Septemvri located in Boulevard 8th September in the city of Skopje—Republic of North Macedonia. Professor Ustijana Rechkoska Shikoska is the Vice Rector of University of Information Science and Technology (UIST) located in Partizanska BB in the city of Ohrid—Republic of North Macedonia. This paper is dedicated to my beloved family.

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  1. Department of Computer Engineering, Epoka University, Rr. Tiranë-Rinas, Km. 12, 1032, Vorë, Tirana, Albania

    Carlo Ciulla

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  1. Carlo Ciulla
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Correspondence to Carlo Ciulla.

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MRI acquisition was consented. Approval was obtained from subjects to use the images for research through the administration of written consent. The research protocol for MRI data acquisition was approved by the Department of Radiology at the General Hospital 8-mi Septemvri located in Boulevard 8th September in the city of Skopje—Republic of North Macedonia. This study was conducted according to principles stated in Helsinki declaration of the year 1964.

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Ciulla, C. Two-Dimensional Z-space Filtering Using Pulse-Transfer Function. Circuits Syst Signal Process 42, 255–276 (2023). https://doi.org/10.1007/s00034-022-02113-4

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