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

2021 ◽  
Vol 27 (8) ◽  
pp. 425-434
Author(s):  
N. N. Nagornov ◽  
Keyword(s):  
Medical Imaging ◽  
Integrated Circuits ◽  
Visual Information ◽  
Linear Time ◽  
Quantization Noise ◽  
Discrete Wavelet ◽  
Wavelet Filter ◽  
High Quality ◽  
3D Images ◽  
Linear Time Invariant

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.).

scholarly journals Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for 3D Medical Imaging

2020 ◽  
Vol 10 (4) ◽  
pp. 1223 ◽  
Author(s):  
Nikolay Chervyakov ◽  
Pavel Lyakhov ◽  
Nikolay Nagornov
Keyword(s):  
Wavelet Transform ◽  
Medical Imaging ◽  
Integrated Circuits ◽  
Discrete Wavelet Transform ◽  
Signal To Noise Ratio ◽  
Maximum Error ◽  
Quantization Noise ◽  
Discrete Wavelet ◽  
Wavelet Filters ◽  
Images Processing

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.

An Improved PD Type Iterative Learning Control Algorithm Based on Wavelet Filter

2014 ◽  
Vol 511-512 ◽  
pp. 898-903
Author(s):  
Yan Xin Zhang ◽  
Ting Xu Zhang
Keyword(s):  
Iterative Learning Control ◽  
Linear Time ◽  
Learning Control ◽  
Iterative Learning ◽  
Wavelet Filter ◽  
Wavelet Theory ◽  
Linear Time Invariant ◽  
Multi Level ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This paper proposes an improved PD type Iterative Learning Control (ILC) algorithm combined with Wavelet theory for linear time-invariant systems with random time delays. The transfer function of multi-level wavelet filter is researched, and the sufficient condition of the convergence is given. Simulation results illustrate the applicability and effectiveness of proposed approach.

Structural changes in silicon-on-insulator material during post-implantation annealing

1986 ◽  
Vol 44 ◽  
pp. 736-737
Author(s):  
C. O. Jung ◽  
S. J. Krause ◽  
S.R. Wilson
Keyword(s):  
Integrated Circuits ◽  
Oxide Layer ◽  
High Speed ◽  
Structural Changes ◽  
Device Fabrication ◽  
Silicon On Insulator ◽  
High Quality ◽  
Radiation Hardened ◽  
Post Implantation ◽  
Very High

Silicon-on-insulator (SOI) structures have excellent potential for future use in radiation hardened and high speed integrated circuits. For device fabrication in SOI material a high quality superficial Si layer above a buried oxide layer is required. Recently, Celler et al. reported that post-implantation annealing of oxygen implanted SOI at very high temperatures would eliminate virtually all defects and precipiates in the superficial Si layer. In this work we are reporting on the effect of three different post implantation annealing cycles on the structure of oxygen implanted SOI samples which were implanted under the same conditions.

Evaluation of fractional order of the discrete integrator. Part II

2020 ◽  
Vol 23 (2) ◽  
pp. 408-426
Author(s):  
Piotr Ostalczyk ◽  
Marcin Bąkała ◽  
Jacek Nowakowski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Output Signal ◽  
Linear Time ◽  
Mathematical Problem ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Input And Output ◽  
Order Difference Equation ◽  
Time Invariant ◽  
Discrete Integrator

AbstractThis is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

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