Medical Image Fusion Based on Joint Sparse Method

I. INTRODUCTION

From the identical scene number of images can be obtained concurrently by utilizing dissimilar sensors. Using the many sensors to identify the picture complete of scene from the obtained images is highly impossible. For this here using image fusion algorithm it will accept the mixing of multiple obtained images to produce number of useful complex image integrating the opposite information from the many sensors, yet, they are out of boundary and of dissimilar declaration. In medical diagnosis we will find the medical imaging. After completing the diagnosis the imaging movements are like magnetic resonance imaging (MRI) and computed tomography (CT) it will gives dissimilar view in the same scene, which can be delay clinical decision making and the diagnostic process. For example MRI gives the perspectives of soft materials, while CT for bone structures evaluation. For accurate diagnosis this inspires the necessary for image fusion by combining the reciprocal information. Three problems to be notified while fusing the images [1] are: 1) the fused image should preserve all the important information needed for further processing. 2) Artifacts should not be introduced in fused image. 3) Noise and unimportant information should be suppressed.

Several dissimilar Greedy approaches using the sparse representation of the signal this signal is presently possible [3],

Sparse representation of signals is now possible utilizing many different Greedy approaches [3], including: 1. Matching Pursuit (MP) [3] 2. Orthogonal Matching Pursuit (OMP) [3], and 3.Stage wise Orthogonal Matching Pursuit (St OMP) [4]. These techniques are used to represent signals with the fewest number of non-zero coefficients. Principal Component Analysis (PCA) [5] is one of the powerful state-of-the-art image fusion approaches in terms of visual inspection and quantitative evaluation metrics. This fusion is carried out by integrating the principal components of images to be fused. Both PCA and Sparse fusion have specific advantages and disadvantages. PCA fusion will enhance the spatial quality but have dense nonzero entries that might represent uninformative features. Sparse fusion preserves important information but high spatial resolution is lacking. This paper proposes a new algorithm inspired by [6], which employs different fusion rules for common and innovative sparse components of the source images. The proposed algorithm utilizes the advantages of both PCA and Sparse representation for fusing common and innovative features of the captured images. This algorithm also overcomes the disadvantages of both PCA and Sparse representation. In this paper, we demonstrate the effectiveness of our proposed method by comparing its results with PCA and Sparse Fusion.

II. SYSTEM DESIGN

As discussed in the previous section, sparsest approximation is achieved through Greedy methods. In this section, we briefly explore the Orthogonal Matching Pursuit algorithm to achieve sparsest representation. These sparse coding algorithms are constructed based on the premise that Dictionary D of size n×k is already known. For effective results, we use phase included DCT (Discrete Cosine Transform) dictionary [7] for our experiment. In this paper, we have customized OMP sparse coding algorithm for fusion purposes.

The ultimate aim of OMP algorithm is to achieve best approximation. The mathematical formula for solving this constraint problem is given by:

(1)

(2)

Where N is the number of non-zero coefficients. Equation 2 represents the definition for solving error constrained problem. Next atom to be added in this iterative framework is the atom which has highest correlation to the residual at each stage. Iteration is performed until it meets the stopping criterion. OMP is due to orthogonalization between atoms in the dictionary D and residual r.

Pseudo Algorithm of OMP

Given: Dictionary D, signal S, and error threshold ϵ

1. Initialize residual r₀=S-Ds⁰, index set I0={} and main iteration is k = k+1 (initial k=0).
2. Using the ideal solution 𝑧_ð‘- = 𝑑_ð‘-^𝑇𝑟^{𝑘−1}/, Calculate the error (ð‘-) = for all i.
3. Update stage: Augmenting the index set 𝐼^𝑘 = 𝐼^{𝑘−1} ∪ {ð‘-₀} (find i₀ of (ð‘-): ∀1 ≤ ð‘- ≤ 𝑚 and (ð‘-₀) ≤ (ð‘-).
4. Update the solution (ð‘-₀)+= 𝑧_ð‘- and residual.
5. If stopping criterion is met, 𝑠 = 𝑠^𝑘; else, apply another iteration.

III. PROPOSED SCHEME

This work proposes a fusion method that employs PCA transformation and sparse transformation. An attempt is made to efficiently utilize the advantages of PCA and Sparse fusion scheme. The proposed fusion framework has been illustrated in Fig.1. Firstly, the common and innovative components are extracted from geometrically aligned multiple images of the same scene. Secondly, different fusion rules are adopted to fuse these coefficients.

The algorithm is summarized as follows:

1) Registered multiple images in an ensemble have one common component and multiple innovative components. Innovative components contain the complementary information from different images of same scene

2) Innovative components of different images i are decomposed into sparse vectors s₁,s₂,s₃,…s_i via orthogonal matching pursuit method described in Figure.1.

Fig.1. Flow of Sparse PCA joint fusion algorithm

3) Combine the sparse coefficients of innovative components using PCA fusion rule, for which the covariance matrix s C of innovative images is calculated as follows,

(3)

Where s₁,s₂ are the sparse vectors of the innovative components. Find the Eigen sparse and normalized Eigen sparse vector of maximum Eigen value. Eigen vector will be used as weightings for innovative sparse vectors to be fused.

4) Fused PCA result I_p is reshaped into a block of 8×8 and each pixel position is the sum of several block values.

Reconstructed image is obtained by dividing each pixel by number of addition operations performed at each pixel.

5) For fusing common component and fused innovative component, the fuse rule of weighted average scheme proposed by Burt et al. [2] is adopted.

IV. EXPERIMENTAL RESULTS

In order to test the performance of the proposed joint fusion algorithm, we compared the quantitative and qualitative results with two state the of art methods. Qualitative measurement is done through visual inspection that considers sharpness and noise suppression. Since the proposed joint fusion uses both PCA and sparse domain, we use PCA, Sparse OMP fusion methods for comparison. For the evaluation, we adopted proposed joint strategy for Multi resolution, Multi focus and Multimode images and compared the results with existing algorithms. Our experiment is carried out with the assumption that the source images are registered already. Fig. 2, shows results of fusion for the case of multi focus images. Based on visual inspection, The Joint PCA Sparse algorithm performs the best since the resultant image contain more geometric structures while sparse fusion comes the second. Result of proposed method seems to contain sharp edges.

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Fig.3, illustrates results of fusion of mutli dosage image results based on three different fusion algorithms. Low dose image seems to suffer from patchiness. As it can be observed, visually, Joint Sparse result shows the details clearly than the Low dose image. Visually, joint fusion resultant seems to be better than other 2 methods. Increasing the dosage might reduce the noise but harm patients. Low dose images are prone to noise. Fusing low dose and medium dose image should suppress the noise and enhance the informative details for precise diagnosis.

Fig.4, illustrates the results of applying two multi modal medical images to three image fusion algorithms. The medical images are MRI and CT image of same scene which have been registered already. CT image provides the information on bone structures and MRI image contains tissue information. Medical image fusion needs great accuracy as it’s used for diagnosis. Hence, multimodal image fusion would give sufficient details necessary for diagnosis. Based on the visual inspection, the Joint Sparse results contain more detail information. Results of PCA seem to have high spatial resolution but they are disappointing in terms of detailed information. Bone details are not visible in PCA resultant image. Sparse result is better but some artifacts are easily observed Reconstructing fused image through joint fusion algorithms seems to be more precise comparatively.

In order to analyze the quality of the algorithms quantitatively, we consider 5 metrics: Mutual Information (MI), PSNR, Correlation, Entropy and Structural Similarity (SSIM) index. Mutual Information shows how much information has been transferred from source images to the resultant images. Entropy shows the amount of important details available in the image.

PSNR is Peak Signal to Noise Ration which is used to measure the reconstruction quality of fused image. PSNR of the fused image If is calculated using the standard formula:

(4)

Where M is the maximum possible pixel value of the image and MSE is the Mean Square error. The SSIM [8] provides structural information of objects and measures the similarity between the two images.

Experiment results are shown in Table.1. Tabulated result demonstrates the effectiveness of the proposed algorithm over existing methods in terms of Qualitative and Quantitative methodologies. We can observe that the results of multimodal image fusion and multi focus image fusion utilizing our proposed fusion strategy outperforms PCA and Sparse fusion. The PCA by itself performs poorer results for all cases.

Table 1

Performance Of Fusion Methods By The Quality Evaluation Metrics

V. CONCLUSION

Medical Image fusion plays an important role in clinical diagnosis. In this paper, a joint fusion modal is proposed based on sparse representation theory and PCA for multimodal and multi dose medical images. Visually and quantitatively, the experimental results show that the proposed method has effectively expressed the geometric structures and edges and has proved to perform better than PCA and OMP fusion. This modal can also be extended to fuse multiple source images from multi resolution, multiple spectral frequencies and multiple modalities.

REFERENCES

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