# Noise and Speckle Reduction in Doppler Blood Flow Spectrograms Using an Adaptive Pulse-Coupled Neural Network

- Haiyan Li
^{1}Email author, - Yufeng Zhang
^{1}and - Dan Xu
^{1}

**2010**:918015

https://doi.org/10.1155/2010/918015

© Haiyan Li et al. 2010

**Received: **1 January 2010

**Accepted: **14 May 2010

**Published: **10 June 2010

## Abstract

A novel method, called adaptive pulse coupled neural network (AD-PCNN) using a two-stage denoising strategy, is proposed to reduce noise and speckle in the spectrograms of Doppler blood flow signals. AD-PCNN contains an adaptive thresholding PCNN and a threshold decaying PCNN. Firstly, PCNN pulses based on the adaptive threshold filter a part of background noise in the spectrogram while isolating the remained noise and speckles. Subsequently, the speckles and noise of the denoised spectrogram are detected by the pulses generated through the threshold decaying PCNN and then are iteratively removed by the intensity variation to speckle or noise neurons. The relative root mean square (RRMS) error of the maximum frequency extracted from the AD-PCNN spectrogram of the simulated Doppler blood flow signals is decreased 25.2% on average compared to that extracted from the MPWD (matching pursuit with Wigner Distribution) spectrogram, and the RRMS error of the AD-PCNN spectrogram is decreased 10.8% on average compared to MPWD spectrogram. Experimental results of synthetic and clinical signals show that the proposed method is better than the MPWD in improving the accuracy of the spectrograms and their maximum frequency curves.

## Keywords

## 1. Introduction

The Doppler ultrasound blood flow signal has been extensively used in clinic to diagnose arterial and venous diseases due to its advantage of being noninvasive [1]. The diagnostic indices which are necessary for a clinical judgment are all extracted from the maximum frequency waveform of the Doppler spectrogram, calculated by using short-time Fourier transform (STFT), and are very useful in diagnosing arterial stenosis or other vascular disease by evaluating the vascular resistance [2]. However, two types of noise are present in the Doppler spectrogram. Firstly, there is background noise, arising from additional frequency components, added to the Doppler ultrasound signals. Additionally, the characteristic granular pattern, known as Doppler speckles, of spectrogram is obtained from Fourier transform-based analyzers when the Doppler signal scattered from cells moving within the same velocity resolution cell interferes with each others [3]. Noise and speckle, which are considered as undesirable properties, directly impact on the subjective study of the maximum frequency waveform extracted from the spectrogram, deteriorate the quality and the perceivable resolution of the indices and the features based on the estimated spectrograms and thus lead to inaccuracy in diagnoses of the artery diseases. Therefore, it is preliminary and essential to remove noise and speckles in the spectrogram of the Doppler ultrasound signal.

Discrete wavelet frames (DWFs), which is superior to methods based on standard discrete wavelet transform (DWT), were used to denoise the Doppler ultrasound signal [4]. Here discrete wavelet frame analysis was first applied to obtain the wavelet coefficients of the Doppler signal at multiple scales. Then, these coefficients were processed by a soft thresholding-based denoising algorithm to remove noise in the signal. In order to improve the adaptability of the threshold, a threshold-based wavelet packet denoising method was employed [5]. This approach, which can adaptively select the threshold, preserved useful high frequency components and offered higher signal-to-noise ratio (SNR) compared with straightforward wavelet-based denoising methods. The matching pursuit (MP) method was also used for improving the SNR of Doppler blood flow signals [6]. Using MP, the denoised Doppler signal was reconstructed by iteratively selecting the components approximate to the signal by a given directory while removing the incoherent residue, which was determined as noise, through a decay parameter-based algorithm. The performance of the MP method was better than those of the DWT and WPs (Wavelet Packets) methods for Doppler ultrasound signal denoising [6]. These denoising methods are effective in removing background noise in the Doppler spectrogram. However, they cannot suppress Doppler speckles in the STFT spectrograms due to the fact that background noise is usually random Gaussian distribution while speckle may be modeled by Rayleigh or distribution [7, 8].

To alleviate the negative effect of the speckle, two types of speckle-reduction approaches, ensemble averaging and filtering [9], have been developed. Ensemble averaging approach is usually achieved by averaging a series of regular spectrograms produced by a flow phantom. However, physiological changes such as heart rate variation make the synchronization of the required waveforms difficult. Moreover, these uncorrelated images may be sampled at different times, from different views, or with different frequencies for the same target. Therefore, ensemble averaging is complex in clinical implementation. The filtering approaches, which treat the Doppler spectrogram as a grayscale image, offer an alternative for clinical applications, and many adaptive filters have been developed. Filtering approaches eliminate the speckle at each pixel based on the local statistics estimated from the Doppler spectrogram. However, the spatial spectral content of sharp intensity variations, such as edges contained in images, extends to infinity and overlaps with noise. Therefore, filters suppress noise while blurring important information-bearing features and fine image details. Meanwhile these speckle reduction methods become ineffective in filtering Doppler background noise and cause loss of the time-frequency resolution in the STFT spectrograms.

In order to effectively suppress Doppler noise and speckle in the STFT spectrograms, a method, called matching pursuit with Wigner distribution (MPWD), was proposed and has obtained good performance in noise and speckle suppression [10]. Using MPWD, a segmented Doppler ultrasound signal was first decomposed by MP greedy iterations for denoising purpose, and then the Wigner distribution was calculated and averaged during each small interval to reconstruct the spectrogram of the denoised signal for Doppler speckle reduction. Since the time interval is small, the Doppler speckle can be effectively smoothed. Meanwhile, this method may not cause the loss of time-frequency resolution in spectrograms as the interval is small enough, and it also does not require invariant heart rate to produce the very regular spectrograms. However, since MP is a greedy iteration and the Wigner distribution is calculated and averaged based on each small time interval, the MPWD is implemented at a high expense of computing complexity. Moreover, since the decomposition continues until the decay parameter is less than a predefined small value and the averaging interval is empirically selected, the MPWD method cannot completely remove all the background noise, and the adaptability of the method is relatively low.

To compensate for the drawback of the previous techniques, a method, called adaptive Pulse Coupled Neural Network (AD-PCNN), is proposed for noise and speckle reduction in the spectrograms of Doppler blood flow signals, while improving the accuracy of the spectrograms and their maximum frequency curves. PCNN biologically inspired from the visual cortex of mammals was first introduced by Eckhorn in [11] and has been widely used for image denoising [12–17]. The pulse capture characteristics of PCNN determine that the neurons that spatially connected and intensity correlated are tend to pulse together, while Doppler noise or speckle, which is independent and uncorrelated to the signal component, can not capture neighboring neurons or can not be captured by neighboring neurons. Thus each contiguous set of synchronously pulsing neurons indicates a coherent structure of the spectrogram, corresponding to the signal component, and the residue, defined as Doppler noise or speckle, can be identified. However, when conventional PCNN is applied for noise and speckle reduction, present theories cannot explain the relationship between the parameters of PCNN mathematical model and the processing effect. Satisfactory results usually require time-consuming selection of experimental parameters. Meanwhile, in a properly selected parametric model, the number of iteration that determines the denoising effect is evaluated by visual judgment, which decreases the efficiency of PCNN. Various improved PCNN models have developed for noise filtering, such as weighted-linking PCNNs [12], which contains four PCNN models to filter Gaussian and impulse noise in images, and a two-step PCNN impulse noise filter [13], which first determines the noisy pixels and then modifies the intensities of noisy pixels in the image. In addition PCNN was combined with other new techniques such as fuzzy, rough set theory and morphology to depress noises [14–17] meanwhile adaptively determining the PCNN parameters. However the computational complexity is therefore increased. These PCNN denoising approaches are proved to be effective in removing isolated noise while the performance of filtering Gaussian noise is degraded since all pixels in an image are contaminated by Gaussian noise. Therefore, conventional PCNN or existing PCNNs cannot be directly applied to suppress noise and speckles in Doppler spectrogram.

In order to improve the adaptability of parameter selection, decrease the computation redundancy of conventional PCNN algorithm, and to be effective in suppressing noise and speckles in Doppler spectrogram, an adaptive PCNN, which contains an adaptive thresholding PCNN and a threshold decaying PCNN is proposed. The proposed PCNN is greatly simplified compared to conventional PCNN and employs an adaptive threshold, which is defined as the basic intensity of the signal component based on the histogram of the spectrogram. The proposed PCNN is a two-dimensional structure with the same size of the Doppler spectrogram, and each neuron is corresponding to a pixel in the spectrogram. The PCNN pulses based on the adaptive threshold decompose the spectrogram into two parts of neurons, coherent structure which is spatially connected and intensity correlated and incoherent component, indicating the signal and noise or speckle in the spectrogram, respectively. After removing a part of noise from the coherent signal, the rule, the Gaussian distribution of the background noise and the Rayleigh or distribution of speckle is broken, and the remained noise or speckle is greatly isolated. Subsequently, the firing matrix of the denoised spectrogram, specifying what time a neuron first fires, is calculated by using the threshold decaying PCNN through iterations, and then the target neuron is detected as a speckle or noise if it fires but more than 50% of the neurons in the linking window do not fire [13], indicating that the intensity of the target neuron is sharply variant compared to other neurons in the linking window. Finally, spectrograms are improved by iteratively suppressing the speckles or noise through a median filter [13], while the signal neurons are kept unmodified. Experiment results show that the proposed method can effectively conserve fine detail information, such as edges while removing speckles and noise. Furthermore, the iteration continues until the firing matrix of the threshold decaying PCNN is unchanged any further. Therefore, the iteration time can be adaptively determined.

The distinctive elements of the proposed method are as follows. ( ) a two-step PCNN model is proposed for noise and speckle suppression in Doppler spectrogram. Firstly an adaptive threshold, taking advantages of the pulse capture characteristics of PCNN and the histogram statistics of the spectrogram, is employed to filter noise from the signal component in the spectrogram. ( ) After a part of background noise is removed by the adaptive threshold PCNN, the remained noise and speckle are greatly isolated and the rule, that background noise is usually Gaussian distribution and speckle is molded by Rayleigh or distribution, is broken. Therefore the isolated noise and speckle can be effectively suppressed by the proposed threshold decaying PCNN, which first detects noise and speckles and then iteratively suppresses the noise and speckles with a median filter. ( ) It is the first attempt to reduce noise and speckles for Doppler ultrasound spectrogram by using PCNN algorithm. The indices, the relative root-mean-square (RRMS) errors of the spectrograms, and their maximum frequency curves between the estimated ones and their corresponding theoretical ones are used to evaluate the performance of the proposed method. Furthermore, effective noise and speckle suppression methods, MP and MPWD [10], are compared with the proposed method.

The remainder of this paper is organized as follows. Section 2 briefly describes the mathematical background of the MPWD and the proposed AD-PCNN noise and speckle reduction methods. Section 3 presents the simulation of the Doppler blood flow signals and experiments on simulated Doppler signals and clinical cases based on two different methods, AD-PCNN and MPWD [10]. Section 4 exhibits experimental results and discussions. Finally, some conclusions are drawn in Section 5.

## 2. Methods

### 2.1. MPWD Noise and Speckle Reduction Algorithm

where
is the residual energy level at the *M* th iteration. The decomposition is continued until the decay parameter does not reduce any further. At this stage, the selected components represent the coherent structures, and the residue represents the incoherent structures in the signal with respect to the dictionary.

*M*coherent structures, a time-frequency energy distribution that is free of cross-terms is derived by adding the Wigner distribution of selected atoms

In the processing, the Doppler signal is divided into successive small segments, each one has a time interval . The Wigner distribution in a time interval, estimated from the denoised signal by (7)-(8), is averaged during this time duration for Doppler speckle reduction in the spectrum. Since the time interval is small, the Doppler speckle, which arises from the interference with each other of cells moving within the same velocity resolution cell, could be smoothed. Meanwhile, this method may not cause the loss of time-frequency resolution in spectrograms as the is small enough, and it also does not require the invariant heart rate to produce the very regular spectrograms, one of the limitations of the ensemble average speckle suppression method. However, since MP is a greedy iteration and the Winger distribution is calculated and averaged based on each small time interval , the MPWD is implemented at a high expense of computing complexity. Moreover, since the decomposition continues until the decay parameter is no more than a predefined small value and the averaging interval is empirically selected, the MPWD method cannot completely remove all the background noise.

### 2.2. Adaptive PCNN Noise and Speckle Reduction Algorithm

The iteration is continued until the firing matrix does not change any further to adaptively determine the iteration time .

During the firing procedure, the intensity value of each pixel and the status of its neighbors (active or inactive) determine what time a neuron fires. Neurons in the same region or with an approximate value tend to fire at the same time. When there are pixels whose intensity values are approximate in their linking region, the pulse output of one of them will fire the others in the linking region, and then produce a firing matrix. Obviously, the firing matrix of PCNN includes the information of the image intensity distribution and the geometry of the original image, which makes noise and speckle detection possible.

When using AD-PCNN for noise and speckle reduction in Doppler spectrogram, in the first step, since the threshold is defined as the basic intensity of the signal, the firing matrix of the adaptive threshold PCNN separates noise, independent and uncorrelated to the signal components, from the signal neurons, which are spatially connected and intensity correlated and then remove the detected noise. Subsequently, the firing matrix of the threshold decaying, indicating what time a neuron first fires, is calculated. If the target neuron fires but more than 50% the neurons in the filtering window do not fire, it denotes that the target neuron has sharp intensity fluctuation and can not capture most of the other neurons in the filtering window; therefore, it is detected as noise or speckle. Finally, the noise and speckle pixels are modified to be the median intensity values in the filtering window and are removed. Since the threshold decaying PCNN detects noise and speckle first and performs intensity variation to the noise and speckle only, the fine image details, such as edges, can be well preserved.

## 3. Experiments

In the experimental study, simulated and clinical Doppler ultrasound signals are used as test sources. The two algorithms, AD-PCNN and MPWD [10], are used to reduce noise and speckle for the simulated Doppler ultrasound signals with a 1024-point duration. The performance of noise and speckle reduction in Doppler spectrogram based on the AD-PCNN is compared with that based on the MPWD method.

### 3.1. Simulation Study

where is the window, and are the discrete time and frequency, respectively, and is the window length.

- (1)
The pixel intensity of the original Doppler spectrogram is normalized to and input to . Initialize , , , , , as a weight-matrix of linking field, and as a temporal matrix. Calculate by (13)–(16).

- (2)
- (3)
- (4)
- (5)
- (6)
- (7)
- (8)
- (9)
In a filtering window, if the target neuron fires but more than 50% the neurons do not fire, then the target neuron is identified as a speckle or noise [13]. Modify the intensity of the target neuron to be the median intensities of the neurons in the filtering window. Otherwise, keep the target neuron unchanged.

- (10)

where and are the simulated original signal and the signal after noise and speckle suppression of the length , respectively. The RRMS errors of the spectrogram and their maximum frequency waveform from 30 simulated signals are calculated before and after noise and speckle suppression and are used to compare the performance improvements of the AD-PCNN algorithm to that by MPWD.

### 3.2. Clinical Study

To obtain the clinical Doppler ultrasound signal, a pulsed Doppler unit of HP SONOS 5500 ultrasound imaging system is used in pulse mode, and the applied frequency of the ultrasound is set to 2.7 MHz. The clinical Doppler signals are recorded from a child's aorta by placing sample volume near the center of the aortic arch. The audio Doppler signals are sampled by using an analog-to-digital Sound Blaster Card in a personal computer, and the sampling rate is set to 22.05 kHz. The objective effect and subjective indices of the spectrogram and their maximum frequency waveform are used to compare the performance of the AD-PCNN and the MPWD noise and speckle suppression algorithms.

## 4. Results and Discussions

The mean and standard deviation of the RRMS errors of the maximum frequency waveforms extracted from the signals with different SNR levels based on the STFT, the MPWD methods, and the AD-PCNN methods (×10^{-3}).

The mean and standard deviation of the RRMS errors of the spectrograms estimated from signals with different SNR levels based on the STFT, the MPWD methods, and the AD-PCNN methods (×10^{-4}).

## 5. Conclusions

A novel method, AD-PCNN has been proposed to enhance Doppler blood flow spectrograms. First, the Doppler spectrograms are denoised by using the adaptive threshold PCNN, which removes background noise from the coherent component with spatiality vicinity and intensity correlation in the Doppler spectrogram and isolates the remained noise. Then, the firing matrix of the denoised spectrogram, calculated by the threshold decaying PCNN is employed to detect speckles. Finally the improved spectrogram is reconstructed by modifying the speckles to be the median intensity in the filtering window. Results from the experiments on simulation and clinical signals show that the proposed method performs effectively in noise and speckle suppression, improves the accuracy of spectrograms and their maximum frequency curves, and achieves better performance than MPWD algorithm. The RRMS errors of the AD-PCNN spectrograms and the extracted maximum frequency of simulated Doppler blood flow signals are decreased by 10.8% and 25.2% on average when compared to MPWD spectrograms on Doppler signals with various SNRs, respectively.

## Declarations

### Acknowledgments

This paper was supported by Grant (60861001) from the National Natural Science Foundation of China, Grant (2009CD016) from the Yunnan Natural Science Foundation, Grant (2008YB009) from the Science and Engineering Fund of Yunnan University, and Grant (21132014) from the Young and Middle-aged Backbone Teacher's Supporting Programs of Yunnan University.

## Authors’ Affiliations

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