Abstract
Intravascular ultrasound (IVUS) imaging is a diagnostic imaging technique for tomographic visualization of coronary arteries and studying atherosclerotic diseases. These medical images are generally corrupted by multiplicative speckle noise due to the interference of the signal with the backscattered echoes. Speckle noise is an inherent property of medical ultrasound imaging, and it generally tends to reduce the image quality; thus, removing noise from the original medical image is a challenging problem for diagnosis application. Trying to reduce this noise should be assist the expert in a better understanding of some pathologies and diagnosis purposes. Recently, several techniques have been proposed for effective suppression of speckle noise in ultrasound B-Scan images. The aim of this paper is, to give an overview about denoising techniques in both spatial and transform domain, and proposed a new despeckling method based on Shearlet and ant colony optimization. To quantify the performance improvements of the speckle noise reduction methods, various evaluation criteria in addition to the visual quality of the denoised images are used. Our results showed that in general Shearlet transform with three different types of threshold selection is faster and more efficient than other techniques. In the case of accurate estimation of the variance of noise, Shearlet transform based on ACO yields acceptable results in comparison with others methods, this technique can obtain a favorable signal-to-noise ratio and successfully improve the quality of images and edges and curves.
Keywords: Ant Colony, Curvelet, Contourlet, Despeckling, Dual-tree Complex Wavelet (DT-CWT), Intravascular Ultrasound (IVUS) Imaging, Shearlet
INTRODUCTION:
Since the birth of computer science, medical imaging devices such as X-ray, CT, MRI, and Ultrasound have been a great help for medicine in general and it particular, which have producing the clinicians with new information about the inside of the human body. Among these imaging techniques, ultrasound imaging is popular as a noninvasive, low cost, portable real time imaging [1],[2].
Intravascular ultrasound (IVUS) imaging is a new modality, works based on the inserted catheter directly into the blood vessel that provides the real-time cross-sectional view of the vessel wall. This technique provides the quantitative assessment of the lumen structure that cannot be visualized by an angiography [3]. IVUS images are generally corrupted by a kind of multiplicative noise called speckle, which is the result of the constructive and destructive coherent summation of ultrasound echoes that degrades the fine details, edge definitions and limit the contrast resolution by making it difficult to detect small and low contrast lesions in body, thus despeckling of medical ultrasound images is a critical pre-processing step for the better diagnosis of some pathologies to investigate the various vessel wall diseases[4],[5].
Various techniques have been proposed to remove the linear and nonlinear noise from the image in order to increase the quality of the image [6],[7]. Most widely different types of filters are used in the applications of speckle noise reduction in ultrasound images. For instance, Mean filter is the least satisfactory method of speckle noise reduction as it results in loss of detail and resolution, it has the effect of blurring the image [8]. The Median filter is used for reducing speckle due to their robustness against impulsive type of noise and edge preserving characteristic. This type of filter produces less blurred images than Mean filter but the disadvantage of this filter is that to find the median it is necessary to sort all the value in the neighborhood into numerical order and its time-consuming because of an extra computation time is needed to sort the intensity value of each set [9]. Wiener filter provides better result in noise reduction, it preserves edges and other high frequency information of the image but requires more computation time and also this type of filter is basically designed for additive noise suppression [10]. To overcome this issue Jain [11] developed a homomorphic filter where the multiplicative speckle noise is converted into additive noise by using the logarithm of input image. A Non-linear estimator such as Bayesian have also developed for noise reduction with outperform classical linear methods [12]. Another denoising techniques such as Multiresolution Bio Lateral Filtering [13], Total Variations [14] and Kernel Regression [15] have been proposed in the past decades, all of these methods estimated the denoised value pixel based on the information provided in a surrounding local limited window, but Buades developed a more efficient algorithm called Non-local Means Algorithm (NLM) based on averaging similar patches in image which exhibits capability to preserve fine details [16].
Over the last decades, there has been abundant interest in Wavelet based method noise reductions in signals and images. Wavelet transforms can achieve the good denoising result but they can capture only limited directional information [17]. Although Wavelets have been extensively used in speckle noise reduction, but it has been shown [18] that speckle denoising using Contourlet provides better results in compare with those of Wavelet Shirinkage and Dual-tree Wavelet transform, because Wavelet is generally the optimal base, when it represents the objective function with point singularity, but it is not the optimal method when it represents the singularity of line or hyper plane. To overcome the exciting drawback of the classical multiresolution approaches such as Wavelets, a kind of multiscale transform based on Ridgelet transform called Curvelet, has rapidly developed by Cande’s and Donoho [19]. This transform can detect the singularity of line and surface well in 2-D dimensional space. Recently, a new denoising method for images based on Shearlet transform has been carried out [20,21]. In this paper, a comparative analysis of the performance of the various despeckling techniques which are widely used for despeckling of ultrasound images, is presented.
This paper is organized as follows: Section (2) describe despeckling methods in both spatial and transform domains used in this paper, section (3) introduced experimental results and data we employed in this paper and in a section (4) we concluded the paper.
METHODS:
Over the years, several techniques have been proposed to reduce the effect of speckle noise within ultrasound images. Among these methods, we are consider a numbers of techniques which is extensively used in both spatial and transform domain, to despeckling ultrasound images in order to compare their performance results.
Spatial domain:
Spatial filtering is a traditional technique to remove noise from the image. In spatial domain the filtering is based on statistical relationship between the center pixel and surrounding pixels, a window known as a mask (kernel) moved over the each pixel of the image and the value of the current pixel is being replaced by the other pixels in the neighborhood, and this procedure continue until the entire image is being covered.
They are different types of filters in this field, which is commonly used for speckle noise reduction, some of the best known of them are:
Median filter: The median filter [9] is spatial nonlinear filter which performs according to move pixel by pixel through the image and compute the medium of all pixels within local window and replacing the center pixel value with the value of the neighborhood pixels. This type of filter produces less blurred images in compare with mean filter, but the disadvantage of this method is the extra computation time needed to sort the intensity value of each set.
Lee filter: Lee filter was one of the earliest filter that working directly on the intensity of the image using local statics and it can effectively preserve edges and features [22]. Lee filtering technique is based on the approach that if the variance over an area is low or constant then the smoothing will not be performed, in otherwise smoothing will be performed if the variance is high.
Img(i.j)=im+W*(C_p-Im) (1)
Where the Img is pixel value at indices (i.j) after filtering, Im is mean intensity of the filter, C_p is the center pixel and W is filter window. The major disadvantage of Lee filter is that it ignores the speckle noise in the areas closest to edges and lines.
Wiener filter: The wiener filter is also known as a least mean square filter perform smoothing on the image based on the computation of local image variance, when the variance of the image is large the smoothing is a little on the other hand, if the variance is small the smoothing will be better. It has capacity to restore images even if they are corrupted or blurred [10].
Wiener filtering which is implements spatial smoothing is given by the following formula:
f(u.v)= 〖H(u.v)〗^*/(〖H(u.v)〗^2+[(Sn (u.v))/(Sf (u.v) )] G(u.v)) (2)
Where H(u.v) is degradation function, G(u.v) is degraded image, Sn (u.v) power spectra of noise and Sf (u.v) power spectra of original image. Wiener filter provides better result in noise reduction, it preserves edges and other high frequency information of the image than the linear filtering but requires more computation time and also this type of filter is basically designed for additive noise suppression.
Non-local Means Algorithm (NLM):
In recent years, patch based image denoising algorithms like Non-local Means filter which proposed by Buades [16] have gotten much more attention to deal with the denoising problems. Most of the denoising techniques degrade or remove the fine details and texture during their performances, but non-local means filtering decrease the loss of the fine image details and also improved the peak signal to noise ratio. This filtering technique is based on a non-local averaging of all pixels in the image and unlike local means filter which takes the mean value of pixels surrounding the target pixel to smooth the image, non-local means algorithm takes a mean of all pixels in the image weighted by the similarity between the local neighborhood of the pixel being processed and local neighborhood of surrounding pixels.
The estimated pixel value ‘ p ‘ using NLM algorithm is computed as a weighted average of all the pixels in the image with the following formula:
NL(V)(p)= ∑_(q∈v)▒〖W(p.q) V(q)〗 (3)
where V is the noisy image, and weights W(p.q) satisfy the following condition 0≤W(p.q)≤1 and ∑_(q∈v)▒〖W(p.q)=1〗 .
Although this denoising method can achieve a good PSNR result but there are still several issues in NLM algorithm which can reduce the efficiency of the algorithm, in particular the performance of this technique depends on the proper selection of the internal parameters such as patch size, search region size and etc, which play a conspicuous role in the performance of NLM algorithm [16].
Transform domain:
Transform domain techniques has got wide spread applications in the field of denoising, in transform domain the image is transformed into frequency domain, the basic assumption is that the transform domain contains the basic elements in different shapes and directions [23]. Despeckling techniques in frequency domain consist of calculating the transform domain coefficients and carrying out filtering of these coefficients based on the threshold value.
The well-known transform domain techniques include Wavelet (Dual-tree Complex Wavelet Transform), Contourlet, Curvelet and Shearlet, which are describe in following section [17,18,19,20].
Wavelet Transform (DT-CWT):
Wavelet techniques are successfully applied to various problem in image processing. Although the Discrete Wavelet Transform (DWT) has lead to many applications but it has been suffered from two main disadvantages [17]:
Lack of shift invariance, which means that small shift in the input signal can cause major variations in the distribution of energy between DWT coefficients at different scales.
Poor directional selectivity due to the separable and real wavelet filters characteristics.
To overcome this limitation, Complex Wavelet Transform (CWT) was proposed [19]. CWT transform employs analytic filters having real and imaginary part which constructed from Hilbert transform. Unfortunately, CWT have not been widely used in image processing due to difficulty designing complex filters which satisfy perfect reconstruction (PR) properties.
An effective approach for implementing analytic wavelet transform was first introduced by Kingsbury in 1998 which is called Dual-tree Complex Wavelet Transform (DT-CWT).
The DT-CWT employs two real DWT ‘s that uses two different set of filters with each satisfy PR properties. The first DWT yields the real part of the transform while the second DWT gives the imaginary part.
DT-CWT decompose a low resolution image into different sub-band images. A one level CWT of an image produces two complex-valued low frequency sub-band images and six complex-valued high frequency sub-band images which is the results of direction selective filters [19].
Figure (1): Dual-tree complex wavelet transform filter bank [17]
Contourlet Transform:
The Contourlet transform which was proposed by Do and Vetterli in 2002, is one of the recent system representation for image analysis [18]. This technique has been applied to several fields in image processing and also offer several advantages over the Wavelet transform in terms of representing geometrical smoothness more efficiently. The Contourlet transform provides a high degree of the directionality, anisotropy and flexible aspect ratio.
This technique employs a double filter bank structure in which at first the Laplacian Pyramid (LP) is used to capture the point of discontinuities and multiscale transform, followed by the directional filter bank (DFB) to link discontinuities to linear structures. DFB was designed to capture the high frequency components present in different directions. Hence the low frequency components were handled poorly, therefore DFB is combined with Laplacian Pyramid (LP) where the low frequency components are removed before applying directional filter bank (DFB).
Owning to the geometrical information, the Contourlet transform achieves better results than Discrete Wavelet Transform (DWT) in image analysis applications. However due to down sampling and up sampling present in both LP and DFB stage, the Contourlet transform is not shift-invariant.
The Contourlet transform decompose image into several sub-bands at multiple scale. Figure (2) shows the block diagram for the Contourlet filter bank. First a multiscale decomposition into octave bands by LP is computed and then a directional filter bank (DFB) is applied to each band-pass channel. The multiscale representation obtained from LP structure is used as the first stage in Contourlet transform.
Figure (2): Contourlet transform double filter bank [ 18]
Curvelet Transform:
Curvelet transform is a kind of multiscale transform which developed by Cande’s and Donoho in 1999 in an attempt to overcome inherent limitation of traditional multiscale representation such as Wavelets [19].
Curvelets provide a sparse representation for images with different geometrical structures which is suitable for representing curve discontinuities. This transform has various structure elements which include the parameters of dimension, location and orientation that cause Curvelet transform became much more efficient than wavelets in the expression of image edges such as geometry characteristics of curve and beeline that has already obtained good results in image denoising.
In the Curvelet domain, the signal is sparse whereas the noise is not. In other word, signal and noise have minimal overlap in the Curvelet domain. This makes Curvelet transform as a superior method for despeckle ultrasound images. The main advantages of Curvelet method is the ability to use relatively small number of coefficients to reconstruct edge details at an image. Each matrix of coefficients is characterized by both angle and scale that is :
C_(m.n)^(j.l)= <f.Φ_(m.n)^(j.l)
(4)
Where Φ is the basis function,j and l are scale and angle respectively and m,n are an index which is limited according to j and l parameters. Full description of the Curvelet transform and it’s mathematical formulation is given in [19].
Figure (3) : Curvelet transform tilling [19]
Shearlet Transform:
Shearlet transform is a non-adaptive multiscale technique which is developed in 2005 to overcome the limitations of Wavelet and Contourlet transform [20,21]. Shearlets are considered as the sloping waveform with directions organized by shear parameters. It was proven that Shearlets are more efficient in compare with Wavelets to represent an anisotropic features such as edges.
A Shearlet is generated by the dilation, shearing and translation of a function ψ, called mother Shearlet in the following way:
ψ_(a.s.t )= a^(-3/4) ψ (A_a^(-1) S_s^(-1) (x-t)) (5)
Where t∈R^2 is a translation, A_a is a dilation matrix and S_s is a shearing matrix defined respectively by:
A_a=(■(a&0@0&√a)) S_s=(■(1&-s@0&1))
The anisotropic dilation A_a controls the scale of shearlets by applying the different dilation factor along two axes and the shearing matrix S_s determines the orientations of shearlets. The Shearlet transform decompose the input image into a number of sub-band images containing a high rate of recurrence sub-band images and low rate of recurrence sub-band images. The magnitude of each and every Shearlet sub-band has the same magnitude as the initial image [20]. The decomposition is highly redundant.
Figure (4) : filter bank structure of Shearlet transform [20]
Figure (4) represent a three level multiscale, shift invariant and multi directional decomposition, since it shows during the first level of decomposition it will give one approximation and n directional detailed bands, the first approximation is given for further level decomposition.
Proposed Method (Shearlet+ACO)
As it was mentioned in the previous section, Shearlet transform was introduced with the expressed intent to provide a highly efficient representation of images with edges which overcomes the limitation of traditional methods in order to despeckling IVUS images. Shearlet shrinkage is an image denoising technique based on the concept of thresholding the Shearlet coefficients. The key challenge of Shearlet shrinkage is to find an appropriate threshold value, which is typically controlled by the signal variance. To tackle this challenge, a new image shrinkage approach called AntShrink introduced in this paper.
Ant Colony Optimization (ACO) [24] is a meta-heuristic method for solving hard combinatorial optimization problems. ACO is a nature-inspired optimization algorithm motivated by the natural collective behavior of real-word ant colonies. The Ant Colony Optimization (ACO) technique is proposed in this paper to classify the Shearlet coefficients and denoising IVUS images.
The basic steps in ACO algorithm can be expressed as follows [25]:
Initialize the position of each ant, as well as the pheromone matrix Ï„^0.
For the construction-step index n=1:N ,
Consecutively move each ant for L steps, according to a probabilistic transition matrix P^((n)) (with a size of M_1 M_2×M_1 M_2).
Update the pheromone information matrix Ï„^((n)).
Make the solution decision according to the final pheromone information matrix Ï„^((N)).
There are two fundamental issues in the above ACO process; that is, the establishment of the probabilistic transition matrix P^((n)) and the update of the pheromone information matrix Ï„^((N)), each of them is presented in detail as follow, respectively.
P_(i,j)^((n))=(〖(τ_(i,j)^((n-1)))〗^α 〖(η_(i,j))〗^β)/(∑_(jϵΩ_i)▒〖〖(τ_(i,j)^((n-1)))〗^α 〖(η_(i,j))〗^β 〗) (6)
τ_(i,j)^((n-1))={█(τ_(i,j)^((n-1))+Δ_(i,j)^((k)) if (i,j) belongs to the best tours@τ_(i,j)^((n-1)), otherwise )┤
(7)
A noisy image in Shearlet domain can be mathematically modeled as [25]:
Y=S*n
where ‘Y’ is the observed noisy coefficients, ‘s’ is the unknown original (noise-free) coefficients, and ‘n’ is assumed to be a noise with a zero mean and a variance σ_n^2. The goal of image denoising is to recover the signal ‘s’ from the noisy observation ‘Y’.
For better comparison, hard thresholds and shrinkage thresholds have also been investigated in this paper [27].
Figure(5): ACO block diagram [25].
EXPERIMENTAL RESULTS:
Data Base:
The IVUS image data set which is used for method validation in this work includes a sequence of IVUS images obtained from [26]. These images, each 500×500 pixels, were acquired using a 30-MHz transducer at a pullback speed of 0.55 m/s and a grabbing rate of 10 frames/s. This process is carried out using the ultrasound system developed by the Volcano therapeutics INC. (model Invision TM, IVG-EE).
Evaluation Criteria:
Several experiments were conducted to evaluated the despeckling ultrasound images, to quantitative analysis for performance, well accepted metrics such as peak signal to noise ratio (PSNR) and mean square error (MSE) which are widely used in evaluating the denoising results of IVUS images, are used.
PSNR is an objective measures which evaluates the intensity changes of an image between the original and enhanced image. The formula for calculating PSNR is given bellow:
PSNR=10 logâ¡ã€–10 (R^2/MSE〗)
Another evaluation criterion is MSE which is computed as:
MSE= 1/K ∑_(i=1)^k▒〖((S_i ) ̂-S_i)〗^2
Note that the high quality image has small value of PSNR and large value of MSE means that image has poor quality. Contrast-to-noise ratio (CNR) and figure of merit (FOM) are an another evaluation metrics which are respectively used to determine image quality and the performance of edge preservation of the image computed as follows:
CNR= |μ^’-μ^” |/(√(σ_1^2 )-σ_2^2 )
FOM= 1/(maxâ¡(N_e.N_i)) ∑_(j=1)^N▒〖 1/(1+d_j^2 a)〗
The results of calculated evaluation criteria for denoising results are summarized in table (1), (2) and (3).
Table (1): The performance metrics results of despeckling methods in spatial domain ( x: original image n: noisy version xr: denoised image)
Noise
Variance PSNR
(x,xr) MSE
(x,xr) Spatial Domain
Lee Filter Median Filter Wiener Filter NLM Algorithm
Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr) Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr) Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr) Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr)
0.04 24.56 0.059 32.24 0.016 53.50 91.07 28.42 0.037 57.71 88.33 27.99 0.039 48.37 85.5 27.68 0.041 55.78 92.29
0.05 23.59 0.066 31.48 0.018 53.40 90.14 27.84 0.040 57.63 87.13 27.20 0.043 48.81 90.01 27.18 0.043 56.66 89.11
0.06 22.83 0.072 30.78 0.019 54.55 89.07 27.41 0.042 58.28 86.70 26.49 0.047 49.26 86.00 26.88 0.045 57.94 88.78
Table (2): The performance metrics results of despeckling methods in transform domain ( x: original image n: noisy version xr: denoised image)
Noise
Variance PSNR
(x,xr) MSE
(x,xr) Transform Domain
DT-CWT Contourlet Curvelet Shearlet
Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr) Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr) Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(xxr) Psnr
(x,xr) Mse (x,xr) Cnr
(x,xr) Fom
(x,xr)
0.04 24.56 0.059 27.45 0.029 52.85 79.04 30.00 0.024 53.67 88.77 30.84 0.031 51.28 88.73 32.72 0.017 54.30 92.42
0.05 23.59 0.066 27.22 0.030 53.11 81.93 29.17 0.026 54.08 90.20 29.29 0.036 51.51 88.82 32.17 0.018 53.91 90.57
0.06 22.83 0.072 26.89 0.031 53.40 80.25 29.08 0.028 54.26 89.32 28.19 0.042 51.45 88.29 31.60 0.019 54.74 89.37
Based on the results in tables (1) and (2), the higher PSNR in both spatial and transform domain, is obtained by the Lee filter and Shearlet transform respectively that indicates the effectiveness of these proposed method for IVUS despeckling.
In this paper, the ACO optimization algorithm is used to find an appropriate threshold value and denoising IVUS images. For better comparison, hard thresholds and shrinkage thresholds have also been investigated. The results of calculated evaluation criteria for denoising results are summarized in table (3).
Table (3): performance metrics results of denoising methods in different type of Shearlet transform ( x: original image n: noisy version xr: denoised image)
Noise
Variance PSNR
(x,xr) MSE
(x,xr) Shearlet-Hard Shearlet-Shrinkage Shearlet-ACO
Psnr (x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr) Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr) Psnr
(x,xr) Mse
(x,xr) Cnr
(x,xr) Fom
(x,xr)
0.04 24.56 0.059 34.83 0.023 53.91 92.44 26.96 0.046 52.78 90.08 29.80 0.029 52.66 93.75
0.05 23.59 0.066 34.56 0.023 54.29 90.86 26.02 0.051 52.83 86.65 28.99 0.037 52.31 91.92
0.06 22.83 0.072 33.98 0.025 54.55 88.89 25.23 0.056 53.08 86.66 28.17 0.040 53.67 93.06
According to the result of table (3), in general Shearlet transform based on ACO yields acceptable results in compare with others methods for despeckling IVUS images.
The results of the threshold methods show that, ACO based Shearlet denoising method yields acceptable results in the accurate estimation of noise variance point of view, comparing to the other despeckling methods for IVUS images. Shearlet based ACO obtain a favorable signal-to-noise ratio and can successfully improve the quality of images and edges and curves.
In addition to this performance metric, the visual inspection of the denoised images is usually used for denoising evaluation.
In order to visualize the better inspection of despeckling results, the noise-free, noisy and denoised images resulting from the mentioned despeckling methods are shown in figure (6).
Original IVUS image Noisy image ( variance =0.06)
De-noised images
Median Filter Lee Filter Wiener Filter
Non-Local Means Algorithm Dual-tree Wavelet Contourlet
Curvelet Shearlet
Shearlet-Hard Shearlet-Shrinkage Shearlet-ACO
Figure (6), Qualitative result of various despeckling techniques
CONCLUSION:
Intravascular ultrasound (IVUS) imaging is used to study the arterial wall structure, the evaluation of atherosclerotic diseases and diagnosis aspects. These medical images are generally corrupted by multiplicative speckle noise. The main objectives of this paper are, to give an overview about despeckling techniques in both spatial and transform domain, and also proposed a new Shearlet shrinkage despeckling technique based on Ant Colony Optimization (ACO). The proposed despeckling technique has been successfully applied to solve many combinatorial optimization problems (time-frequency domain). The evaluation of results support the conclusion that the Shearlet transform with three different type of threshold selection is faster and more efficient comparing to the other available techniques such as spatial filters or wavelet based methods. Shearlet transform based on ACO include various additional functionalities which make this method yields acceptable results in compare with others methods, this method can obtain a favorable signal-to-noise ratio and mean square error (PSNR,MSE) and successfully improve the quality of images and edges and curves (CNR,FOM).
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