An image reconstruction technique based on IPSO-DWT under varying crack

Abstract

Image Reconstruction is an important fragment in image processing. It is used to reconstruct the image which is corrupted by noise or that has some scratched regions. In order to improve the reconstruction effectiveness of the existing methods a new image reconstruction technique based on DWT and IPSO is proposed in this paper. The proposed technique is composed two main stages (i) training stage (ii) investigation stage. In training phase, initially the input cracked image is reconstructed by the DWT (Discrete wavelet Transform) method by selecting optimal threshold value using well known optimization technique as IPSO (Improved Particle Swarm Optimization). These selected threshold values are stored in the Threshold Database and they are subjugated in the image reconstruction process. In investigation stage, the threshold value is selected based on the crack level of the testing image. The proposed method is implemented in MATLAB with various cracked images. The performance of the IPSO and DWT based image reconstruction technique is checked with existing PSO and average filtering image reconstruction technique in order to prove the efficiency of the proposed method. However, our proposed methodology provides better intuitive and high-quality reconstructed image for the noisy images than the existing method, in terms of peak signal-to-noise ratio (PSNR).

Keywords

Image reconstruction Improved Particle Swarm Optimization (IPSO)Discrete Wavelet Transform (DWT)Peak Signal-to-Noise Ratio (PSNR)

1 Introduction

Image reconstruction embraces the overall image formation function and furnishes a base for the successive phases of image processing. The underlying objective revolves round the retrieval of the image data lost during the task of image formation. As against the image enrichment, where the appearance of an image is fine-tuned to fulfill certain subjective standards, image reconstruction represents an objective method to restore a degraded image according to mathematical and statistical models [1]. Image reconstruction is a hilltop task as significant variations in the image are likely to be highly blurred, resulting in just trivial modifications in the calculated data. This leads to two vital associated risks related to image reconstruction. First, noise variations may be misguided for genuine signal. Further, it is quite difficult to discriminate between competing image models if the divergences in the data models attained from them by blurring are well-within the measurement noise [2]. The reconstruction methods, in turn, are segmented into two such as the analytic and iterative techniques. The analytic reconstruction approaches usher in a direct mathematical solution for the formation of an image. The iterative methods, on the contrary, are dependent on a further precise depiction of the imaging task leading to a highly intricate mathematical solution entailing manifold measures to realize an image [3].

Image reconstruction issue involves precisely modeling the physics of the imaging task. This is quite different from several general purpose image processing methods such as the image compression which are not essentially limited by similar parameters. Still, several traits of the latter algorithms like the speed and robustness, goes a long way in boosting the image reconstruction methods [4], which have surfaced as the most amazing devices in computer vision systems and several other applications requiring sharp images attained from noisy and otherwise tainted ones. Simultaneously, the total variation (TV) formulation has been established to furnish a sound mathematical foundation for various vital functions in image reconstruction, like de-noising, in-painting, and de-blurring [5].

In statistical image reconstructions for ECT (emission computed tomography), we are faced with the following three significant features of the paradox such as the statistical model, the regularization method, and the iterative maximization/minimization algorithm. A precise statistical model is a must-have for a superb reconstruction [7, 9]. Further, the client generally holds certain a-priori data on the image to be reconstructed. The relevant data can be integrated the regularization technique to generate “reasonable-looking” images. At the end of the day, a sound technique is a sine-qua-non to guarantee that a superb reconstructed image is well-within reach in a reasonable time-frame [6]. Of late, diffuse optical tomography has emerged as a novel new medical imaging modality with potential applications in functional imaging of the brain and in breast cancer recognition, amid identical applications. This technique sets upon itself the task of recovering the optical parameters of blood and tissue from boundary measurements of light transmission in the visible and near-infrared range. The reconstructed images of the spatial distribution of tissue constraints can be linked directly to physiologically significant features like blood and tissue oxygenation state [8, 10].

The rest of the paper is organized as follows. In Section 2, a brief review is made about the recent research works related to image reconstruction process that is emphasized in relation to its problem statement. Next, Section 3 details the proposed image reconstruction technique with necessary mathematical formulations. Section 4 discusses about the implementation results and comparative results whereas as in Section 5 concludes the paper.

2 Related works

A few of the most recent literature works in image reconstruction are reviewed below.

Laura B. Montefusco et al. [12] got a bunch of bouquets for launching novel reconstruction techniques, targeted at the recovery of the misplace data either by utilizing the spatio-temporal correlations of the image series, or by thrusting appropriate restraints on the reconstructed image volume. The vital contribution of their research centres round the blending of this technique in a compact sensing structure by using the gradient sparsity of the image volume. The consequent inhibited 3D minimization challenge has been successfully addressed by means of a penalized forward–backward splitting method that paves the way for a convergent iterative two-phase process. In the initial phase, the rule accords are updated with the sequential behavior of the data acquisitions and subsequently, a genuine 3D filtering strategy employs the spatio-temporal correlations of the image sequences. The consequent Non-linear Filtering Compressed Sensing (NFCS)-3D algorithm turns out be to a very common and appropriate one for various types of medical image reconstruction hassles. Further, it shines with the quality of swiftness, stability, and invariably ushers in superb reconstructions, especially in the case of highly under sampled image sequences. The cheering outcomes of various arithmetical tests have vouchsafed the optimal performance of the innovative technique and proved without any iota of doubt that it maintains a clear, unsurpassable edge over the hi-tech algorithms.

Brent A. Williams et al. [13] have been instrumental in launching a reconstruction estimator based on maximum a posteriori probability (MAP) evaluation to recuperate the traditional samples from noisy scatterometer dimension. This technique empowers the scatterometer noise distribution to be properly accounted for in the reconstruction task. The MAP and traditional reconstruction techniques have been applied to the Sea Winds scatterometer and the Advanced Wind Scatterometer, and the effective resolution of various techniques has been evaluated. The outcomes of MAP approach have been in line with the entrenched scatterometer image reconstruction (SIR) algorithm. The MAP technique has incredibly augmented the resolution at the expense of enhanced noise. Though a thread-bare noise-versus-resolution tradeoff evaluation is not envisaged in this document, the novel structure allows for a more common treatment in relation to the ad hoc tuning constraints of the SIR algorithm. Hakan Erturk et al. [14] have explained that thermal interfaces are faced in several thermal management applications and interface materials are employed to reduce thermal contact resistance originating from solid-solid contact. For opto-electronic equipments, the quality of the thermal interface is vital for setting aside the produced heat for appropriate thermal administration. Deficiencies in the thermal interface bring in extra thermal resistance in the thermal path, and therefore have to keep under check. Identification of deficiencies in the thermal interfaces is highly essential in the course of the assembly procedure progress. Imaging methods like the X-ray computerized tomography or scanning acoustic microscopy which entail costly devices and considerable processing during are indispensable. Thermal tomography in conjunction to IR thermometry can be employed as a cost-effective option to these methods. The viability of thermal tomography for non-destructive characterization of thermal interfaces has been offered after taking into consideration several image reconstruction techniques such as the iterative perturbation algorithm, Levenberg Marquardt algorithm, and the regularized Newton Gauss algorithm, and they are observed to be competent to characterize the thermal interface layer.

Ravi Saharan et al. [15] have explained that digital images can be deemed as set of pixels. If a single image is segmented into more than one component, then these subparts are considered as segments for an image. Blending of 2D fragments of an image means that, these image segments have to be reassembled. The blending of segments to rebuild images and objects is a challenge linked to various applications, such as archeology, medicine, art restoration, and forensics. They have wholly focused their attention on 2D Image Reconstruction by blending two 2D segments. This method is in accordance with the data produced from the boundary and from the color contents of the two segments. Local curvature has been estimated to achieve alteration independent coordinates. In accordance with this data, analysis has been carried out to get maximum matching parts among segments. In the long run, longest matching parts have been blend to achieve a single image.

Peyman Rahmati et al. [16] have illustrated the initial clinical outcomes by means of the level set based reconstruction technique for electrical impedance tomography data. The level set based reconstruction approach permits the reconstruction of non-smooth interfaces between image regions, which are typically smoothed by conventional voxel based reconstruction techniques. They have designed a time difference formulation of the level set based reconstruction technique for 2D images. The novel reconstruction technique has been executed to rebuild clinical electrical impedance tomography data of a slow flow inflation pressure-volume maneuver in lung healthy and adult lung injury patients. Images from the level set based reconstruction technique and the voxel based reconstruction approach have been analyzed and contrasted. The cheering outcomes have illustrated beyond any doubt the competence of the technique in turning out superlative reconstructed images, along with an enhanced capability to rebuild sharp conductivity modifications in the distribution of lung ventilation by means of the level set based reconstruction technique.

Kanakaraj et al. [17] proficiently propounded a sparse parameter dictionary structure for super-resolution image reconstruction, which blends the feature patches of high-resolution and low-resolution images by means of sparse parameter dictionary coding. This method has been able to fabricate a sparse association between middle-frequency and high-frequency image elements, and comprehends concomitantly match searching and optimization techniques. Analysis and contrast with sparse coding technique has proved that sparse parameter dictionary is more dense and competent. Sparse Kernel-Single Value Decomposition algorithm has been executed for optimization to fasten the sparse coding procedure. Several tests with real images have illustrated that sparse parameter dictionary coding has outclassed all the traditional learning-based super-resolution algorithms in respect of PSNR.

Shan Gai et al. [18] have presented a new feature extraction method based on quaternion wavelet transform (QW T). The QWT yielded one shift invariant magnitude and three phases based on quaternion algebra. The generalized Gaussian density (GGD) was applied to capture the statistical characteristics of QW T coefficients. The neural network was used as classifier in the framework of banknote classification. Experimental results demonstrated its effectiveness and the proposed method obtained a higher recognition rate in the banknote classification.

Shan Gai et al. [19] have presented a study of the reduced quaternion wavelet transform (RQWT) which has one shift-invariant magnitude and three angle phases at each scale from digital image analysis application. A new multi scale texture classifier which uses features extracted from the sub-bands of the RQWT decomposition was proposed in the transform domain. The proposed method can achieve a high texture classification rate. The experimental results can demonstrated the robustness of the proposed method and achieve a higher texture classification accuracy rate than a famous wavelet transform based classifier.

3 Proposed DWT and IPSO based image reconstruction technique

Image Reconstruction is to recover the original image from its given horrible form. An image that is corrupted by noise or that has some scratched regions will be reconstructed. Different reconstruction methods were utilized for performing the image reconstruction process. In our proposed Image Reconstruction Technique initially the face images are gathered from the face database d _b. The database face images which are affected by cracks with different variances are reconstructed using IPSO with DWT method.

$\begin{matrix} Let d_{b} & = & {d_{x 1}, d_{x 2}, d_{x 3} \dots d_{xi}}; \\ i & = & 1, 2, 3, \dots N be a database images . \end{matrix}$ (1)

Where N is the total number of images in the database d _b.

d _x is the one of the image in the database d _b.

The image d _x which is affected by cracks c with different crack variance levels vr is d _x (c _vr), where vr is randomly generated interval.

The innovative Image Reconstruction method contains two stages such as the training stage and investigation stage. In the training stage, with a view to wipe off the cracks from the given input image d _x (c _vr) initially we perform DWT to the crack image. Subsequently, we proceed for the selection of optimal threshold value, which is realized by the famous optimization technique known as IPSO. In the investigation phases at diverse divergence levels the cracks are applied to the testing image. Thereafter, the testing images with difference crack divergence levels are saved and analyzed with the analogous threshold values in the threshold database. In the testing, image reconstruction is obtained by analyzing testing image divergence level with threshold database DT. In accordance with the crack divergence levels the optimal threshold values op (td) are chosen from the database DT and applied to the testing crack image to arrive at the reconstructed output image. The basic structure of our proposed Image Reconstruction technique is given in Fig. 1.

The proposed Image Reconstruction technique consists of two stages namely

Training phase

Applying DWT

Selection of optimal threshold value

Investigation phase.

3.1.1 Training phase

In training phase,

Apply cracks on the training images at diverse crack variance levels

Evaluate the average pixel values for all pixels by means of the following equation:

avg = \frac{1}{N_{p}} \sum_{x = 1}^{N_{p}} p_{x}

(2)

Where p _x - pixel value

N _p- Number of neighbor pixel value of the pixel

Replace the pixels which are assaulted by the cracks using the value obtained in step 2.

The image obtained in the above process is denoted as d _x (c _vr) and DWT is applied on the image subsequently.

3.1.2 Applying Dwt

Apply Discrete Wavelet transform (DWT) to the cracked image d _x (c _vr) to obtain the DWT image. Discrete Wavelet transform (DWT) is a mathematical tool for hierarchically decomposing an image. The transform is based on small waves, called wavelets, of varying frequency and limited duration. Wavelet transform provides both frequency and spatial description of an image. DWT is the multiresolution description of an image the decoding can be processed sequentially from a low resolution to the higher resolution. The DWT splits the signal into high and low frequency parts. The high frequency part contains information about the edge components, while the low frequency part is split again into high and low frequency parts. For each level of decomposition, we first perform the DWT in the vertical direction, followed by the DWT in the horizontal direction.

There are 4 sub-bands: LL1, LH1, HL1, and HH1. (L = Low and H = High).

The LL sub band contains the approximation of the original image while the other sub band contains missing details. Hence LL band is the most significant band for decomposition. $y (n) = \sum_{k = - \infty}^{n - 1} x [k] h [2 n - k]$ (3)

After applying the Discrete Wavelet transform (DWT) to the given input image d _x (c _vr). We obtained the DWT decomposed image $d_{x}^{d} (c_{vr})$ as a result. In next stage for the obtained DWT image find the optimal threshold value by using IPSO. The process of optimal threshold value selection is described inSection 3.2

3.2 Optimal parameter selection using IPSO

3.2.1 Improved Particle Swarm Optimization (IPSO)

Particle swarm optimization (PSO) is a population-based optimization algorithm modeled after the simulation of social behavior of birds in a flock. The algorithm of PSO is initialized with a group of random particles and then searches for optima by updating generations. Each of the particles are flown through the search space having its position adjusted based on its distance from its own personal best position and the distance from the best particle of the swarm. The performance of each particle, i.e. how close the particles is from the global optimum, is measured using a fitness function which depends on the optimizationproblem.

According to PSO, there are two different types of versions are used. The first is “individual best” and the second is “global best”.

Particle swarm optimization (PSO) represents a population-based optimization technique designed by replicating the social character of birds in a flock. The PSO starts with a group of arbitrary particles and then proceeds to search for optima by refreshing generations. Each particle is flown through the search space having its location adapted in accordance with its distance from its own personal best position and the distance from the best particle of the swarm. The feat of each particle regarding how near the particles are from the global optimum, is evaluated by means of a fitness function based on the optimizationissue.

As per the PSO, there are two diverse kinds of versions used, such as the “individual best” and the “global best”.

“Individual best”: It is the individual best selection technique which assesses each individual position of the particle to its own best position pbest, only. The data regarding the other particles is not employed in this pbest.

“Global best”: It is the global best selection technique, which obtained the global knowledge by enabling the shifting of the particles which includes the location of the best particle from the entire swarm. In addition, every particle exploits its skills from foregone events in respect of its own best solution. This is the version of the algorithm employed in thisdocument.

In a n-dimensional search space R ⁿ, each particle i, flies. Every particle i individually contains the following three vectors. The parameters such as smallest size of area and smallest threshold cut value are taken as the particles in the search space.

The current position of the ith particle in the search space.

Location of the best solution found so far by the ith particle in the search space.

The direction for which the particle i will travel (the current velocity).

The personal best position of an particle is denoted as, pbest. The particles in the search space contain its co-ordinates that are related with the fitness as the best solution. The value of fitness is stored in it. It is the pbest value. The pbest value of a particle i is the best position that the particle has seen so far. If fitness specifies the fitness function means, then the pbest value of the particle i is updates as follows. $pbest = {\begin{matrix} p_{i} = x_{i} \\ p_{fitness} = x_{fitness} \end{matrix} if x_{fitness} > p_{fitness}$ (4)

Another location obtained by any of the particle in the population is the gbest value, which is the global version of the particle swarm optimizer and is the overall best value. The global best position of the whole swarm is denoted as, gbest. $gbest = best (pbest)$ (5)

Any particle can move in the direction of its personal best position to its best global position in the course of each generation. The moving process of a swarm particle in the search space described as: $\begin{matrix} V_{i} = w^{*} V_{i} + C_{1 b} * r_{1} * \\ (P_{besti} - S_{i})^{*} P_{besti} + \\ C_{1 w} * r_{2} * (S_{i} - P_{worsti})^{*} P_{worsti} \\ + C_{2} * r_{3} * (G_{besti} - S_{i}) \end{matrix}$ (6)

In Equation (6),

w- Inertia weight

V _i- Velocity of the particle

C _1b- acceleration coefficient in best position

C _1w- acceleration coefficient in worst position

P _besti- the best position of the particle i

S _i- Current position of the particle

P _worsti- the worst position of the particle i

r ₁, r ₂, r ₃- Uniformly distributed random numbers in the range [0 to 1].

3.2.2 IPSO in terms of Parameters Optimization phases

Generate the particle randomly: For a population size m, produce the particles arbitrarily.

Describe the fitness function: The fitness function selected has to be deployed for the parameters in accordance with the current population.

Initialize gp and bp

At the outset, the fitness value is evaluated for each particle which is set as the Pbest value of each particle.

Among the Pbest values, the best one is chosen as the gp value.

Velocity Computation: The new velocity is estimated by means of Equation. [6]

Swarm Updation: Estimate the fitness function once more and refresh the bp land gp values. If the new value is superior to the earlier one, substitute the old by the new one. And also choose the best bp as the gp.

Criterion to stop: Go on with the step till the solution is sound enough or till maximum iteration is arrived at.

In our modified PSO, in addition with the pbest value, the personal worst location of the particle that is denoted as pworst is also used. The previously seen worst locations of the particle are represented by this pworst value. While updating the velocity, pworst value is also taken into consideration along with the difference between the personal best position of the particle and the current location of the particle. By including pworst value, the particle can detour its previous worst location and try to select the better position. The additional exploration capacity to the swarm is provided by the behavior of the worst particle. Usage of both pbest and pworst values reduces the time taken for convergence, so our proposed IPSO process made the best solutions very faster and better achievement of an optimal threshold op (td) is obtained.

3.3 Investigation phase

During investigation phase more number of testing image are utilized to investigate the performance of reconstruction method.

Step: 1 Initially at different variance level the cracks are applied to the testing image.

Step: 2 Afterward the testing images with difference crack variance levels are stored and compared with the corresponding threshold values in the threshold database.

Step: 3 In testing, image reconstruction is achieved by comparing testing image variance level with threshold database DT.

In accordance with the crack variance levels the optimal threshold values op (td) are chosen from the database DT and applied on the testing crack image to get the reconstructed output image.

4 Results and discussion

The proposed image reconstruction technique is implemented in the working platform of MATLAB (version 7.12) with machine configuration as follows

Processor: Intel core i5

OS: Windows xp

CPU speed: 3.20 GHz

RAM: 4GB.

The proposed image reconstruction technique based on IPSO with DWT performance has been analyzed by exploiting different images taken from the database with different crack variance levels. Figure 3 shows some sample images fetched from the database.

The input Images with varying crack levels are reconstructed using the proposed image reconstruction technique based on IPSO-DWT method. Reconstructed images are shown below in Fig. 4.

4.1 Performance analysis

Moreover, in comparative analysis, our proposed IPSO-DWT based reconstruction technique performance is compared with the existing PSO-DWT and average filtering image reconstruction technique. The comparison result shows that our IPSO-DWT has given more PSNR than the Existing PSO-DWT and average filtering technique. The performance result of our comparison techniques has been shown below in Table 1.

4.1.1 Discussion

Table 1 illustrates the PSNR value of Proposed IPSO-DWT and Existing PSO-DWT, Average Filtering Five Different Images with crack Variance 0.1, 0.2, 0.3 and 0.4.our proposed IPSO-DWT technique achieves better image reconstruction performance than the Existing PSO-DWT and average filtering technique. The crack variance level 0.1, our proposed PSO-DWT technique attains the average PSNR value of 17.73078 but the Existing PSO-DWT and average filtering technique produce the image with the average PSNR value of 17.71688 and 15.19898 respectively. When increasing the crack variance levels 0.2, 0.3 and 0.4, the proposed PSO-DWT technique gets high PSNR value when compared the existing techniques. However, in all crack variance levels our proposed PSO-DWT technique produce good reconstructed image results than the existing PSO-DWT and average filtering technique in terms of their PSNR and image quality. Hence our proposed IPSO-DWT image reconstruction techniques produce good performance results in the image reconstruction process.

The comparison graph of our proposed IPSO-DWT image reconstruction technique with existing PSO-DWT, Average Filtering image reconstruction techniques is illustrated in Fig. 5.

4.1.2 Discussion

From the Fig. 5 it has been crystal clear that the PSNR value of the proposed IPSO-DWT method is higher than the existing Existing PSO-DWT, Average Filtering methods. Even though the crack variance level varies from 0.1 to 0.4 the proposed technique has not much vary in PSNR range but the existing PSO-DWT, Average Filtering has shown more variation in PSNR range. Hence from the performance analysis graph it has been clear that our proposed PSO-DWT technique has given high performance reconstructed image results in terms of PSNR than the existing PSO-DWT, Average Filtering techniques.

5 Conclusion

In this document, we are glad to launch an innovative an image reconstruction technique with the aid of IPSO-DWT method. The IPSO has been utilized to optimize the threshold value selection in DWT. The optimized threshold values have been utilized in image reconstruction process and the quality image is obtained from the DWT. The proposed image reconstruction technique performance has been analyzed by exploiting different images with different crack variances. The experimental results proved that our proposed IPSO-DWT has given high performance reconstructed image results in terms of PSNR. Moreover, in comparative analysis, our proposed technique performance is compared with the Existing PSO-DWT, average filtering image reconstruction technique. The comparison result shows that our IPSO-DWT has given more PSNR than the Existing PSO-DWT, average filtering technique Therefore by utilizing the IPSO-DWT technique; our proposed image reconstruction technique proficiently reconstructed the images

References

Carsten Denker, Alexandra Tritschler and Mats Lofdahl, “Image Reconstruction”, Encyclopedia of Optical Engineering, New York, 2004

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