Sampling Technique for Fourier Convolution Theorem Based k-space Filtering

Ciulla, Carlo; Xhaferri, Ilva; Deek, Fadi P.; Muzhaqi, Endri; Veljanovski, Dimitar; Shikoska, Ustijana Rechkoska; Risteski, Filip A.

doi:10.22541/au.167655859.96254660/v2

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“…Table I in [14] shows the computer programs implementing the filters. For each convolving function, table II in [14] shows the number of runs used to verify the sampling technique for k‐space filtering. The data set comprises 30 magnetic resonance imaging (MRI) images (see Table II in [14]).…”

Section: Resultsmentioning

confidence: 99%

“…For each convolving function, table II in [14] shows the number of runs used to verify the sampling technique for k‐space filtering. The data set comprises 30 magnetic resonance imaging (MRI) images (see Table II in [14]). This number is inclusive of the number of images that were filtered by at least one (or more) of the 15 filters used in this paper (4 proposed, 10 used for comparison, and the elliptical filter).…”

Section: Resultsmentioning

confidence: 99%

“…Twenty runs were used for the comparison across the three filters: Bessel, Butterworth, and Chebyshev. Table IV in [14] summarizes the filter parameters for these comparisons.…”

Section: Resultsmentioning

confidence: 99%

“…Rows (i) and (j) show, from left to right: Sinc‐shaped filtering function , Z‐space of the Sinc‐shaped filtering function, and the filtered image. The parameters of these experimental sessions are reported in Table V in [14]. The table at the bottom of the figure shows the computer programs implementing the filters.…”

Section: Resultsmentioning

confidence: 99%

“…This section presents qualitative and quantitative evaluation of the 4 methods presented in this paper with other existing methods. Figures 11 and 12, and Figure 5 in [14] provide the analysis. The four filters proposed by this research were compared to 10 additional methods.…”

Section: Resultsmentioning

confidence: 99%

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Sampling technique for Fourier convolution theorem based k‐space filtering

et al. 2023

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This research presents a sampling technique for Fourier convolution theorem (FCT) based k-space filtering. One polynomial function and three transfer functions were selected: (1) Gaussian, (2) Bessel, (3) Butterworth, and (4) Chebyshev. The functions were sampled on the image grid, and they are called filtering functions. Each filtering function was multiplied by the Sinc function to obtain the "Sinc-shaped convolving function." The k-space of the Sinc-shaped convolving function is calculated by direct Fourier transform (FT) and it is featured by a central region. This central region of the k-space is rectangular in its shape because it is consequential to the direct FT of the product between the filtering function and the Sinc function. Low-pass and highpass filtering is obtained by inverse FT of the pointwise multiplication between the k-space of the departing image and the k-space of the Sinc-shaped convolving function. A variety of cut-off frequencies, bandwidth, sampling rates, and numbers of poles of the filters were verified as effective to filter the images. Filtering strength can be modified by fine-tuning the size of the central rectangular k-space region of the Sinc-shaped convolving functions. K-space analysis of departing images and filtered images provide additional evidence of effective filtering. Moreover, k-space filtering was compared to Z-space filtering using the extension of the FCT to Zspace. The novelty of this research is the sampling technique used to determine the Sinc-shaped convolving function. The sampling technique uses fine-tuning of bandwidth and sampling rate to determine the strength of the k-space filter.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Twenty runs were used for the comparison across the three filters: Bessel, Butterworth, and Chebyshev. Table IV in [14] summarizes the filter parameters for these comparisons.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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