Abstract
Denoising and compression of 2D and 3D images are important problems in modern medical imaging systems. Discrete wavelet transform (DWT) is used to solve them in practice. We analyze the quantization noise effect in coefficients of DWT filters for 3D medical imaging in this paper. The method for wavelet filters coefficients quantizing is proposed, which allows minimizing resources in hardware implementation by simplifying rounding operations. We develop the method for estimating the maximum error of 3D grayscale and color images DWT with various bits per color (BPC). The dependence of the peak signal-to-noise ratio (PSNR) of the images processing result on wavelet used, the effective bit-width of filters coefficients and BPC is revealed. We derive formulas for determining the minimum bit-width of wavelet filters coefficients that provide a high (PSNR ≥ 40 dB for images with 8 BPC, for example) and maximum (PSNR = ∞ dB) quality of 3D medical imaging by DWT depending on wavelet used. The experiments of 3D tomographic images processing confirmed the accuracy of theoretical analysis. All data are presented in the fixed-point format in the proposed method of 3D medical images DWT. It is making possible efficient, from the point of view of hardware and time resources, the implementation for image denoising and compression on modern devices such as field-programmable gate arrays and application-specific integrated circuits.
Highlights
(5) allows determining the minimum quality of 3D medical images Discrete wavelet transform (DWT) depending on the wavelet used, bit-width of wavelet filters coefficients and bits per color (BPC)
We proved that Formulas (6)–(9) can be used to determine the minimum bit-width of wavelet filters coefficients for which the result of 3D images
DWT reaches high (PSNR ≥ 40 dB for images with 8 BPC, peak signal-to-noise ratio (PSNR) ≥ 60 dB for images with 12 BPC and PSNR ≥ 80 dB for images with 16 BPC) and maximum (PSNR = ∞) quality respectively depending on the wavelet used
Summary
The typical medical imaging system consists of three components (Figure 1): data acquisition, data consolidation and data processing. The data acquisition card, which filters incoming data, is the most cost-sensitive system card. A diagnostic imaging system will consist of multiple data acquisition cards. Once the data is compensated and filtered in scanners, it is sent to the data consolidation card for buffering and data alignment. Once the data has been collected, it is sent to the image processing cards [18]. These cards perform heavy-duty filtering and the most algorithm-intensive image reconstruction. Modern field-programmable gate array (FPGA) devices are widely used in data consolidation, and image processing for sophisticated application algorithms implementation including pattern recognition, image enhancement and data compression [19,20]
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