Defining of the Minimum Wavelet Filter Coefficients Bit-Width for 3D Medical Imaging

Abstract

Medical imaging uses a variety of modalities to provide visual information about a patient. Various methods are used to process this data. Many of them are based on discrete wavelet transform (DWT). Its use will allow effective denoising and compression of 2D and 3D images. This paper proposes a new approach to linear time-invariant wavelet filtering using quantized filter coefficients when using which the computational errors have different signs and allow to partially compensate each other as a result of which the processed image is of high quality. The analysis of the quantization noise of the direct multilevel DWT filter coefficients is carried out. The derived formulas demonstrate the relationship between the quantization accuracy of these coefficients and the processing quality of digital 3D images. The derived formulas for calculating the minimum accuracy of the wavelet filter coefficients representation in the computing devices memory allow minimizing the effect of quantization noise on the result of 3D images processing. Modelling of 3D medical tomographic images DWT processing showed that a decrease in the ratio of the average voxel brightness to the maximum allowable value with increasing color depth of images leads to faster achievement of high quality compared to the results of theoretical analysis with an increase in the value of the scaling degree of the wavelet filter coefficients. The obtained theoretical and practical results open up the possibility for reducing the computational complexity of software and hardware implementation of wavelet processing of 3D medical visual data on modern microelectronic devices (field-programmable gate arrays, application-specific integrated circuits, etc.).