A case study on medical image enhancement based on II curvelet

Abstract

A method is presented in this paper for medical image enhancement based on II curvelet. After the wavelet decomposition of medical image, we continue to break down the high-frequency sub-images, in order to get more detailed information. We have also designed the corresponding gain weight function for the edge enhancement of low-frequency sub-images, using II curvelet to extract the edge information, which has advantages over the normal curvelet transform. This method has overcome the disadvantages of the present medical image enhancement algorithm based on wavelet theory, for instance, (1) most of the present methods only decompose the low-frequency sub-images to get detailed information; (2) they can not well extract the tumors or other large areas of edge information of medical images. In simulation experiments, we enhanced the mammography X-ray images of breast provided by Heilongjiang Provincial Tumor Hospital, and compared our algorithm with several traditional image enhancement methods. The results shows that with our enhancement algorithm based on II curvelet, the textures and edges of the image can be reflected clearly, and the calcifications in the image are independent, at the same time, this method has the superiority when enhancing the images which have been added noise to.

Keywords

Image enhancement high frequency sub-image decomposition wavelet transform gain weight II curvelet transform

1. Introduction

Breast cancer is one of the main causes of death in women in the world. The incidence of breast cancer has reached a million, and it is spreading from the middle-aged women to the younger. As a kind of tumor, breast cancer derives from the abnormal division of cells, which is not only harmful to the breast tissue itself, but also can spread to other organs, such as the lung, the liver, etc. Studies have found that the mortality from breast cancer is increasing year by year, and ends up the top of diseases in women. Therefore, this field needs attention and research.

The key to control breast cancer is to discover it at an early time. Now the most important means for prevention is taking X-ray photography regularly. During the inspection, rays are released by an X-ray emission instrument, and then go through the breast, finally the unabsorbed rays come to the film and form an image, which is a grayscale image. The reflection of normal tissues is white, while adipose tissue is expressed as black. Mammography X-ray is a kind of X-ray, which has a high contrast, so we can obtain clearer images with it.

Calcifications and tumors are the main anomalies in mammography X-ray images, which can be the basis for breast cancer diagnosis. The calcification syndrome are the points that are mostly scattered or distribute in clusters, while the tumor syndrome mainly refers to hyperplasia, cancer, etc. in the images, and they are mainly located at the edge of the curve in images. Human tissue, light, noise and other factors have an impact on the quality medical image, as a result, the features in the images are not very clear, which can add difficulties for doctors to distinguish between diseased tissue and normal tissue, so we need to process the X-ray films to make calcifications and masses tumors clearer, in order to reduce the difficulties causing by low sharpness of the images in disease diagnosis, and reduce the misdiagnosis rate.

At present, many image processing methods [1–3] are widely applied in practice, but they may be ineffective for medical images, especially breast X-ray images herein, on which a large number of scholars in this field have done researches [4–9]. Most wavelet-based medical image enhancement algorithms pay only attention to the processing of wavelet coefficients [10], and they all decompose the low frequency sub-image to get details, completely ignoring the high frequency sub-image processing. Studies in literature [5] have shown that the high frequency sub-image still contains a lot of details after the wavelet decomposition, which can give doctors and patients more information, such as the potential possibilities for diseases to worsen or improve. These information can be important references for physicians to develop further treatment. Scholars have studied how to choose the wavelets against the large amount of calculation when extracting the edges after the wavelet decomposition, and finally found that symmetric orthogonal wavelets have unique advantages in this regard [6]. Literature [8] has given four kinds of image enhancement methods for detecting calcifications in breast X-ray examinations, aiming to find the most suitable algorithm for the calcifications processing, and the results shows that the wavelet method is the one.

Image enhancement algorithm based on wavelet can enhance the calcifications well, but when it comes to tumor syndrome, curvelet transform is needed as it is capable of detecting curves. Based on the ideas of the researchers mentioned above, literature [11] presents an image enhancement method based on high-frequency sub-image decomposition using antisymmetric bi-orthogonal wavelet (‘wavelet high-frequency sub-image method’ for short). In literature [11], curvelet is used to detect the edges, and wavelet is used to refine the edges, so differing from traditional methods, it can be real-time and does not need a large amount of computation when extracting the edges, at the same time, the calcifications are independent and there are no agglomerations or large whitish blocks. All of above are the advantages of the algorithm in literature [11].

We take use of the idea of literature [11] in this paper. Wavelets only have advantages in processing the points when extracting the edges, but the effect is not very well for tumors or other lager areas of edge information in the image, so we introduce the II curvelet to extract the edges, which has superiority over the traditional curvelets. That is to say, wavelet transform is used to processing the calcifications as it is excellent for processing points, while the II curvelet transform is used to handle the tumors. We have designed the corresponding gain weight functions, which can adjust the parameters itself to make sure the images will not be distorted. In simulation experiments, we tested histogram transformation method, wavelet nonlinear enhancement method, histogram equalization method and the method in Chapter 4.1 in literature [11], and the breast mammography X-ray images are provided by doctor Gao from Heilongjiang Provincial Tumor Hospital. The result shows that the II curvelet enhancement algorithm in this paper has many advantages over others, for example, the textures and the details of the edges are clear; the calcifications in the images are independent; the effect is much better than that of the method in literature [11] when processing the images which has been added noise to.

2. Image enhancement algorithm based on II curvelet transform

Image enhancement algorithm based on wavelet can enhance the calcifications well because it has great effect on singularities, but the it is not efficient for the tumor syndrome in the images in our study. This paper thus exploit the II curvelet transform to improve the algorithm for image enhancement.

2.1. II curvelet transform

Let $f (t_{1}, t_{2})$ be the sub-image that needs curvelet transform, namely the low-frequency sub-image after wavelet decomposition in step one (in literature [11], Chapter 4, Section 4.4). Assume that it is in Cartesian coordinate system, and $0 ⩽ t_{1}, t_{2} ⩽ n$ , then the formula of discrete curvelet transform will be: $\begin{matrix} (1) & c^{D} (j, l, k) = \sum_{0 ⩽ t_{1}, t_{2} ⩽ n} f (t_{1}, t_{2}) φ_{j, l, k}^{D} [t_{1}, t_{2}] . \end{matrix}$

In (1), $φ_{j, l, k}^{D} [t_{1}, t_{2}]$ is the curvelet function, and D indicates that it is discrete.

We choose a band-pass function $ψ (ω_{1}) = \sqrt{ϕ {(ω_{1} / 2)}^{2} - ϕ {(ω_{1})}^{2}}$ , in which $0 ⩽ ϕ ⩽ 1$ , and make the follow definitions: $\begin{matrix} (2) & \{\begin{matrix} ψ_{j} (ω_{1}) = ψ (2^{- j} ω_{1}), \\ \tilde{U} (ω) = ψ_{j} (ω_{1}) V_{j} (ω), \end{matrix} j > 0 . \end{matrix}$

Because $ω = (ω_{1}, ω_{2})$ , $ω_{1} > 0$ .

We get $\begin{matrix} (3) & V (S_{θ_{l}} ω) = V_{j} (2^{[j / 2]} ω_{2} / ω_{1} - l) . \end{matrix}$

In (3), $S_{θ_{l}} = [\begin{matrix} 1 & 0 \\ - tan θ_{l} & 1 \end{matrix}]$ ; $tan θ_{l} = l \cdot 2^{[j / 2]}$ , $l = - 2^{[j / 2]}, - 2^{[j / 2]} + 1, \dots, 2^{[j / 2]} - 1$ . Then the segmentation of the frequency range has been done. When $θ_{l} \in [- π / 4, π / 4)$ , we have: $\begin{matrix} {\tilde{U}}_{j, l} (ω) = ψ_{j} (ω_{1}) V_{j} (S_{θ_{l}} ω) = {\tilde{U}}_{j} (S_{θ_{l}} ω) . \end{matrix}$

In regard to the discrete curvelet transform for low-frequency sub-images, we can quickly get the curvelet coefficients using the normal USFFT algorithm.

2.2. Low-frequency sub-image enhancement based on curvelet

After processing the low-frequency sub-image with II curvelet transform theory, we usually choose nonlinear ways to enhance the curvelet coefficients. The gain function is: $\begin{matrix} (4) & y_{c} (x, σ) = \{\begin{matrix} 1, & x < c σ, \\ \frac{x - c σ}{c σ} {(\frac{m}{c σ})}^{p} + \frac{2 c σ - x}{c σ}, & x < 2 c σ, \\ {(\frac{m}{x})}^{p}, & 2 c σ ⩽ x < c σ, \\ {(\frac{m}{x})}^{s}, & x ⩾ m . \end{matrix} \end{matrix}$

In (4), x is the curvelet coefficient; σ is the standard deviation of the noise; p is the metric of nonlinear transform; m is the threshold, while s is the dynamic compression range, and c is a parameter.

There are four parameters that need adjustments in the above enhancement algorithm, so the experiment can be rather complex. This paper combines the advantages of curvelet and wavelet, detecting the edges by calculating the modulus and the phase angle with the curvelet coefficients after the curvelet transform of low-frequency sub-image.

The process of enhancement is as shown in Section 4.1.2 of Chapter 4 in article [11]. This paper aims at enhancing medical images, which means highlighting the detailed information of the edges in images, and making sure the images will not be distorted. In order to enhance the details of edges in breast X-ray images, it must meet the following formula: $\begin{matrix} (5) & \begin{matrix} E (H_W_{2^{f}} f (x, y)) = w_{j} H_W_{2^{f}} f (x, y), \\ E (V_W_{2^{f}} f (x, y)) = w_{j} V_W_{2^{f}} f (x, y) . \end{matrix} \end{matrix}$

The characteristics of the wavelet coefficient modulus of the noise are that the modulus will be small if the scale is large, and the modulus is big when the scale is small. What is more, taking the distortion of medical images into consideration, we have designed the following gain function: $\begin{matrix} (6) & w_{j} = \frac{c_{0}}{1 + e^{J - j}} + 1 . \end{matrix}$

During the experiment, the only parameter $c_{0}$ in the gain function has good adjustability.

2.3. The procedure of image enhancement algorithm based on II curvelet transform

The first step, decomposition of the image:

(1)
take multiscale decomposition for $f (x, y)$ ;
(2)
continue to decompose the high-frequency sub-images in (1), and calculate the maximum value $T_{max}$ and minimum value $T_{min}$ of the sub-band coefficient modulus;
(3)
take discrete curvelet transform for the obtained low-frequency sub-images in (1).

The second step, denoising and enhancement of the high-frequency sub-image
(1)
use nonlinear methods to reduce the noise in the sub-images obtained after the decomposition of high-frequency sub-image;
(2)
enhance the sub-image in which the noise has been reduced;
(3)
reconstruct the processed image for the first time with inverse Haar wavelet transform.

The third step, enhancement of the low-frequency sub-image
(1)
calculate the modulus and the phase angle using curvelet coefficients after the curvelet transform;
(2)
detect the edges using edge detecting algorithm along with the data obtained in last step;
(3)
enhance the detected edges using (6) as the gain function;
(4)
reconstruct the low-frequency sub-image with inverse curvelet transform after the enhancement of edges.

The fourth step, wavelet reconstruction of the image: reconstruct the whole image with inverse transformation based on antisymmetric bi-orthogonal wavelet;

The fifth step, post processing with nonlinear gray value stretching method.

In this algorithm, except (3) in the first step and (1), (4) in the third step, the processing methods are the same with that in article [11], Chapter 4, Section 4.1. The flow chart is shown in Fig. 1.

Fig. 1.
Flow chart of the algorithm.
2.4. Evaluation of the effect of image enhancement

So far, effect of image enhancement has not a recognized evaluation criteria, the main reason is that effect of image enhancement is related to the human visual characteristics, it is difficult to objective quality and subjective quality of image well together. Currently, there are two commonly evaluation indicators: PSNR (peak signal to noise ratio) and contrast gain [10]

(1)
PSNR: $\begin{matrix} (7) & PSNR \approx 10 {log}_{10} \frac{255^{2}}{\sum {(\hat{f} - f)}^{2} / N} . \end{matrix}$

In (7), $\hat{f}$ denotes the gray values of the enhanced image, while f denotes the gray values of the original image, and N is the total number of pixels, that is to say, the size of the image.
(2)
Contrast gain: The contrast ratio of an image is the difference value between the maximum and minimum of the gray values. The image appears to be more clear when the contrast ratio is relatively large, and the image looks blurry if the contrast ratio is relatively small. $\begin{matrix} (8) & C = \frac{\hat{f} - \hat{b}}{\hat{f} + \hat{b}} / \frac{f - b}{f + b} . \end{matrix}$

In (8), f denotes the average gray value of the foreground of the original image, and b represents the average gray value of the background of the original image, while $\hat{f}$ refers to the average gray value of the foreground of the enhanced image, and $\hat{b}$ is the average gray value of the background of the enhanced image.
3. Simulation experiment

We have taken simulation experiments with breast mammography X-ray images provided by doctor Gao from Heilongjiang Provincial Tumor Hospital. We enhanced the image with the image enhancement algorithm based on II curvelet transform, which has been described in Section 2.3 in this paper, and compared the result with that of the method in literature [11] (Chapter 4, Section 4.1) and that of the traditional image enhancement algorithms (histogram transformation method, wavelet nonlinear enhancement method and histogram equalization method). The size of the original image 256 × 256, and the experiment was carried out with Matlab. The original image is as shown in Fig. 2, and Fig. 3 is the original image after adding noise.

Fig. 2.

The original image.

Fig. 3.

The original image after adding noise.

3.1. The parameters in II curvelet method and other enhancement methods

We took image enhancement experiments on the original image (Fig. 2) and the image with noise (Fig. 3), using the algorithm based on II curvelet transform presented in this paper, and took comparison and analysis between the results of our method and others. The parameters are:

(1)
The parameters in the wavelet method in article [11]: choose spline wavelet $Bior 3.5$ as antisymmetric bi-orthogonal wavelets; decomposition scale $J = 3$ for the first decomposition; decomposition scale $K = 2$ for further decomposition of high-frequency sub-images based on Haar wavelet; $c_{0} = 1$ . According to the designed gain function, the gain coefficients in edge enhancement can be calculated as $ω_{31 k} = ω_{32 k} = ω_{33 k} = 1.50$ ; $ω_{21 k} = ω_{22 k} = ω_{23 k} = 1.26$ ; $ω_{11 k} = ω_{12 k} = ω_{13 k} = 1.12$ ; $k = 1, 2, 3, 4$ ; the size of the refining area in edge extracting algorithm $a = 3$ .
(2)
The parameters in image enhancement based on wavelet nonlinear enhancement method: use $db 4$ for wavelet transform; the threshold $T_{1} = 0$ , $T_{2} = 0.7$ ; the gain coefficient $k_{1} = 0.6$ , $k_{2} = 2$ ; the range of gray scale is $[0.3, 0.7]$ .

3.2. Experiment one

Figure 4(a)–(e) shows the results of the original image in Fig. 2 enhanced by various ways:

Fig. 4.

The results of the original image enhanced by various ways.

The original Fig. 2 is enhanced by various of methods, and the indicators of the results are shown in Table 1.

According to Fig. 4 and Table 1, the effect of image enhancement based on our II curvelet method and the indicators are all better than that of other enhancement methods. The textures and the edge details can be clearly displayed, while the calcifications in the image are independent. Compared to wavelet method in article [11], the mean and the variance are almost the same, but the contrast gain of our II curvelet algorithm is better, which indicates that the II curvelet algorithm presented in this paper can better enhance the original image in Fig. 2 than wavelet method, but the effect is not significant.

3.3. Experiment two

Figure 5(a)–(b) shows the results of Fig. 3 enhanced by II curvelet method in this paper and wavelet method in literature [11].

For further study on the advantages of II curvelet algorithm, we added noise to the original Fig. 2 and got Fig. 3, then enhanced the images with II curvelet algorithm and wavelet algorithm. The results of the experiment are shown in Fig. 5(a) and (b), from which we can see that although the result is obviously better than the original image after enhancement by wavelet method in literature [11], we still see a large amount of noise points in the image, which may be mixed up with the calcifications in the area we mainly observe. On the contrary, our II curvelet algorithm can wipe out all the noise points after enhancement, and the effect of the image is excellent. Visually, II curvelet algorithm has great advantages over wavelet method in literature [11] on enhancing the images with noise.

The process of adding noise brings up lots of noise information, while the process of reducing noise in image enhancement can dislodge most of the noise information, so the mean value is sure to drop. Similarly, because the gray value of the noise is large, the contrast gain will increase. Thus the mean value and the contrast gain cannot exactly reflect the effect of image enhancement. As a result, we need to use PSNR (peak signal to noise ratio) introduced in (7) in Section 2.4 of this paper to compare the effects of image enhancement. PSNR is a frequently-used index for valuation of images.

For the results of the above experiments, the enhancement indicators of the wavelet method in literature [11] and the II curvelet method in this paper are displayed in Table 2.

Table 1
Comparison of the indicators of the enhancement results

Enhancement methods Mean MSE Contrast gain

The original image 11.3324 32.6635 0.9026

Histogram equalization 214.2995 10.7915 0.1255

Histogram transformation 13.8402 44.6749 0.9033

Nonlinear wavelet method 12.4845 31.4559 0.9048

Wavelet method in literature [11] 11.3780 33.0971 0.9079

II curvelet method 11.3248 32.5473 0.9097

Enhancement methods	Mean	MSE	Contrast gain
The original image	11.3324	32.6635	0.9026
Histogram equalization	214.2995	10.7915	0.1255
Histogram transformation	13.8402	44.6749	0.9033
Nonlinear wavelet method	12.4845	31.4559	0.9048
Wavelet method in literature [11]	11.3780	33.0971	0.9079
II curvelet method	11.3248	32.5473	0.9097

Fig. 5.

Image enhancement of Fig. 3 based on II curvelet in this paper and wavelet method in [11].

Table 2

Indicators of the results after image enhancement for Fig. 3

Enhancement methods	PNSR
The image after adding noise	90.9607
Wavelet method in literature [11]	96.8343
II curvelet method in this paper	100.6442

From Table 2 we can see that after the processing of the image with the two methods, the SNR (Signal to Noise Ratio) of II curvelet method is the highest, according to which we can infer that II curvelet method is much better than wavelet method designed in literature [11] on processing images with noise, but the superiority is feeble on processing the original images.

4. Conclusion

This paper presents a medical image enhancement method based on II curvelet, and takes experiments on breast mammography X-ray images provided by Heilongjiang Provincial Tumor Hospital, then compares the enhancement result with that of several frequently-used image enhancement methods, aiming at making the enhanced images meet the needs of practical application. The following works have been done:

(1)

Proposed an algorithm that continues to decompose the high-frequency sub-image and enhances it based on the fact that the high-frequency sub-image still contains a large amount of detailed information after wavelet decomposition.

(2)

In order to make sure the image will not be distorted during the enhancement of the edges, designed gain weight functions for edge enhancement. The parameter $c_{0}$ in the gain weight function can adjust by itself to get better experiment results.

(3)

Wavelets only have advantages in processing the points when extracting the edges, but the effect is not very well for tumors or other lager areas of edge information in the image, so we introduced the II curvelet to extract the edges.

(4)

Carried out simulation experiments on the proposed II curvelet enhancement method, and compared it with traditional enhancement methods, such as histogram transformation method, wavelet nonlinear enhancement method, histogram equalization method and the method in literature [11]. The result shows that with the method in this paper, the textures and edge details can be clearly reflected, while the calcifications in the images are independent. What is more, our method has superiority over that in literature [11] when processing the images which has been added noise to.

Footnotes

Acknowledgements

This work is supported by foundation of Harbin Institute of Technology (No. GFQQ57500052), Heilongjiang Natural Science foundation (No. A201112).

References

[1] Kashiha

Bahr

Ott

Moons

C.P.H.

Niewold

T.A.

Ödberg

F.O.

and Berckmans

, Weight estimation of pigs using top-view image processing, in: Image Analysis and Recognition, Lecture Notes in Computer Science, Vol. 8814, Springer, Cham, Switzerland, 2014, pp. 496–503.

[2] Belean

Terebes

and Bot

, Low-complexity PDE-based approach for automatic microarray image processing, Medical and Biological Engineering and Computing 53(2) (2014), 99–110.

[3] Yang

S.-Y.

and Kim

J.-J.

, Implementation of a reading assistive computer system using image processing techniques, in: 2014 International Conference on IT Convergence and Security, ICITCS 2014, 2014.

[4] Du

Zhang

Guo

and Dai

, Adaptive enhancement of medical X-ray image based on glowworm swarm optimization algorithm with Cauchy mutation, ICIC Express Letters 8(10) (2014), 2837–2842.

[5] Yang

and Sun

, Medical image enhancement algorithm based on wavelet transform, Electronics Letters 46(2) (2010), 120–121.

[6] Sumana

I.J.

Islam

M.M.

and Zhang

D.S.

, Content based image retrieval using curvelet transform, in: 2008 IEEE 10th Workshop on Multimedia Signal Processing, 2008, pp. 11–16.

[7] Lao

Zheng

and Zou

, Statistical representation of high-dimensional enhancement fields with application to consistent enhancement of chest X-ray images, in: Medical Imaging 2013: Image Processing, Proceedings of SPIE, Vol. 8669, 2013.

[8] Starck

J.L.

Murtagh

and Candes

E.J.

, Gray and color image contrast enhancement by the curvelet transform, IEEE Transactions on Image Processing 12(6) (2003), 706–717.

[9] Scholkmann

Revol

Kaufmann

and Kottler

, Comment on ‘A new method for fusion, denoising and enhancement of X-ray images retrieved from Talbot–Lau grating interferometry’, Physics in Medicine and Biology 60(2) (2015), 925–928.

10.

[10] Cheng

H.D.

Min

and Zhang

, Automatic wavelet base selection and its application to contrast enhancement[J], Signal Processing 90(4) (2010), 1279–1289.

11.

[11] Su

, The study of medical image enhancement based on wavelet, Harbin Institute of Technology, 2009.