This paper presents a novel method utilizing wavelets with particle swarm optimization (PSO) for medical image compression. Our method utilizes PSO to overcome the wavelets discontinuity which occurs when compressing images using thresholding. It transfers images into subband details and approximations using a modified Haar wavelet (MHW), and then applies a threshold. PSO is applied for selecting a particle assigned to the threshold values for the subbands. Nine positions assigned to particles values are used to represent population. Every particle updates its position depending on the global best position (gbest) (for all details subband) and local best position (pbest) (for a subband). The fitness value is developed to terminate PSO when the difference between two local best (pbest) successors is smaller than a prescribe value. The experiments are applied on five different medical image types, i.e., MRI, CT, and X-ray. Results show that the proposed algorithm can be more preferably to compress medical images than other existing wavelets techniques from peak signal to noise ratio (PSNR) and compression ratio (CR) points of views.

Compressing patient’s medical images is a rising demand nowadays in medical organizations due to the needs to archive and transfer large numbers of high resolutions images. Indeed, maintaining those images costs organizations powerful servers, wide network bandwidth and backup storage devices. The problem arises here is concerning the nature of these data itself, medical images need special care when performing compression. Losing important medical details in images may affect medical diagnose for patients. Therefore, any improvement in image compression methods would help storing and transferring medical history properly.

Many compressing algorithms have been proposed in this context, some of them utilizes wavelet family transforms. Haar wavelet method is a member of the family, it is considered as a popular image compression method due to its simplicity comparing to others. Nonetheless, the main disadvantages of the Haar wavelet is features discontinuity that leads to difficulties for simulating continuous signals [

In this paper, a modified Haar wavelet (MHW) algorithm for medical images compression is introduced. The algorithm combines Haar wavelet with PSO as a threshold value selection method. This modification assists in compressing medical image to maintain its purity and preserve fine details while keeping compression ratio high.

The proposed algorithm begins by subdivide the input image into four frequency subbands: one approximation and three detail coefficients. Haar wavelet is modified for this task in order to work with

A threshold is utilized for reducing search space of the coefficients while nine thresholds assigned to their positions are selected to represent subbands (one for each subband). We use these thresholds as particle candidates for the PSO algorithm. PSO is updated by the global best position (gbest) for all details subband and local best position (pbest) for a subband. We developed the fitness value to terminate the PSO to reach a target threshold. The proposed algorithm is implemented using various types of medical images with different sizes, and it is compared with other existing wavelets techniques. The algorithm achieved better result from PSNR and CR point of views.

This work is organized into five sections: Section 1 introduced the work. In Section 2, related work is depicted. Section 3 describes the proposed algorithm. The performance evaluation is shown in Section 4. We provided the experimental results in Section 5. Finally, the conclusion is presented in Section 6.

Medical image compression techniques can be categorized into two main types depending on the redundancy removal way, namely Lossless et al. [

Wavelet transform considers a well-known technique that can work as lossy or lossless compression based on calculating thresholds in the details subbands [

Rao et al. [

From the stated methods, we have noted that there is no universal algorithm for providing an optimal compression. Each algorithm has its own specific drawbacks like compressing ratio, speed, image types, or memory usage. Therefore, effort is needed in order to overcome such drawbacks.

In this section, we describe the proposed algorithm for medical image compression. The novelty of this algorithm is the use of POS for the shrinkage of the transforming coefficients.

Haar wavelet transform is the simplest orthogonal wavelet transform, and it is computed by iterating difference and averaging between odd and even pixels of digital images. Haar wavelet transform can be utilized in various ways for compressing images by decomposing its matrix to sparser one [

Instead of performing Haar wavelet levels on rows then perform the same step on resulting matrix (on columns) as what in [

where values of

For reconstruction, we can gain

In a similar way, the reconstruction equation:

We use thresholding process in order to reduce searching space of coefficients. First, subbands coefficients are evaluated by applying MHW on the input image to obtain four subbands details (coefficients). This means that the positions in

Redistributing the coefficients of this matrix to be:

where

In order to reach optimal PSNR, MHW is applied again to LH, HL and HH subbands to get 12 subbands: three approximation, and nine details. The approximation subbands (LL) includes the important information (approximation) as shown in

Secondly, we select an element _{ij}

where

Also,

PSO has appeared as a rising algorithm for solving various optimization challenges iteratively [

In our methods, the nine positions are the population assigned to particle values (i.e., a threshold value for a subband) as in

where

The population is updated by

where _{best}

The proposed algorithm starts by input a given image to MHW transformation. MHW works on detailed subbands instead of approximation subbands. Then, the subbands are reconstructed while thresholding process is completed; particle swarm optimization is used for thresholding details of subbands based on the fitness function. Briefly, the proposed algorithms can be described as the following steps:

Step 1. Applies MHW (

Step 2. Applies MHW (

Step 3. Uses threshold (

Step 4. Finds input particles that consist of nine positions assigned to threshold values.

Step 5. Applies PSO (

Step 6. Updates the position and velocity (

Step 7. Updates the

Step 8. Repeats to reach 9th subband.

Step 9. Finds the best threshold

Step 10. Reconstructs the compressed image

After reconstructing the subbands (thresholds matrix) by applying the transformation (

MSE measures the error between two images. Root mean squared error or RMSE calculated using the square root of MSE. MSE can be evaluated for monochrome images by:

where

PSNR represents the ratio between original signal variance and reconstruction error variance. PSNR is expressed in Decibel scale. The PSNR used as a measure of the reconstruction quality gained during image compression process. Compression methods aim to maximize PSNR values.

Assuming pixels are represented using eight bits while 255 represents the maximum pixel value of the image, PSNR values takes range between zero and infinity, infinity for perfect identical images and 0 for images that have no commonality.

CR is defined as the ratio between the original image size and compressed image size.

where

The absolute value of the change in method results, divided by the average of them, then multiplied by 100. it is calculated for finding percentage differences between method performances.

In this section, various compressing methods are compared aiming to compress medical images. We experimentally study the performance of these methods, where the performance is assessed using a wide number of medical images of different sizes from MRI and CT types. To run this experiment, five different grey-scale medical images were used: MRI for

The images were compressed by existing Haar, Coiflet, Daubechies, Biorthogonal, Dmeyer, Symlets, and the proposed algorithm. Then, the inverse transformation was used to construct the final images (constructed image). All method outputs were compared quantitatively and qualitatively.

In this subsection, we use numerical indicators to evaluate the methods.

CR | PSNR | MSE | |
---|---|---|---|

Haar | 2.5682 | 26.3769 | 2.82337 |

Coiflet | 1.7829 | 40.0881 | 0.66357 |

Daubechies | 2.0491 | 30.1964 | 0.68032 |

Biorthogonal | 2.0239 | 32.0253 | 0.10366 |

Symlets | 2.9024 | 35.0815 | 0.20952 |

Dmeyer | 1.1393 | 30.2387 | 0.68699 |

The proposed algorithm (LH–HL–HH) | 14.8163 | 0.87829 | |

The proposed algorithm (LL–LH–HL–HH) | 24.0887 | 1.1718 | |

Haar | 2.6466 | 25.2462 | 2.17622 |

Coiflet | 2.1025 | 36.6308 | 0.29933 |

Daubechies | 2.3615 | 25.4495 | 0.22804 |

Biorthogonal | 2.406 | 28.2878 | 0.43839 |

Symlets | 2.905 | 29.9912 | 0.64893 |

Dmeyer | 1.359 | 25.9514 | 0.2559 |

The proposed algorithm (LH–HL–HH) | 6.5342 | 0.17241 | |

The proposed algorithm (LL–LH–HL–HH) | 7.1814 | 1.8236 | |

Haar | 2.9457 | 25.0598 | 2.08477 |

Coiflet | 2.3498 | 34.6629 | 0.19026 |

Daubechies | 2.6602 | 31.3664 | 0.89067 |

Biorthogonal | 2.6526 | 32.5322 | 0.11649 |

Symlets | 2.6041 | 26.2899 | 0.27673 |

Dmeyer | 1.5495 | 31.5563 | 0.93049 |

The proposed algorithm (LH–HL–HH) | 4.5104 | 0.87776 | |

The proposed algorithm (LL–LH–HL–HH) | 6.0169 | 1.0795 | |

Haar | 2.5855 | 23.3738 | 1.41404 |

Coiflet | 2.3429 | 37.1228 | 0.33524 |

Daubechies | 2.6775 | 30.1408 | 0.67167 |

Biorthogonal | 2.5292 | 30.4901 | 0.72792 |

Symlets | 2.8059 | 32.1218 | 0.1059 |

Dmeyer | 1.4911 | 30.1177 | 0.66811 |

The proposed algorithm (LH–HL–HH) | 13.3651 | 0.0228 | |

The proposed algorithm (LL–LH–HL–HH) | 21.9901 | 0.6897 | |

Haar | 2.4085 | 29.0192 | 5.18799 |

Coiflet | 1.9801 | 35.5678 | 0.23434 |

Daubechies | 2.2243 | 30.6045 | 0.74736 |

Biorthogonal | 2.3521 | 30.8809 | 0.79647 |

Symlets | 2.3521 | 27.706 | 0.383422 |

Dmeyer | 1.2881 | 30.8763 | 0.795632 |

The proposed algorithm (LH–HL–HH) | 5.6097 | 0.16633 | |

The proposed algorithm (LL–LH–HL–HH) | 8.0881 | 2.2228 |

The proposed methods on the sub details (LH–HL–HH) and (LL–LH–HL–HH) gave better results than the existing wavelets like Haar, Coiflet, Daubechies, Biorthogonal, Dmeyer, and Symlets. The proposed methods are the best whether they are used for compressing MRI or CT types.

When we applied the proposed method (LH–HL–HH) to the MRI images

Similarly, when we applied the proposed method (LL–LH–HL-HH) to the MRI images

When we utilized

In this subsection, a comparison between reconstructed images of the

In this paper, we have introduced a novel algorithm based on merging wavelets and PSO to overcome the medical image compression problems like trade-off between CR and PSNR. Keeping CR high affects PSNR, and vice versa. The algorithm has been designed to keep the PSNR as high as possible using the PSO. It has been applied to challenging applications like MRI, CT, X-ray images in order to prove its efficiency. The output results were compared with the existing wavelets techniques like Haar, Coiflet, Daubechies, Biorthogonal, Dmeyer and Symlets. Applying the algorithm on (LH–HL–HH) keeps the LL subband constant during the decompositions, and that assists in achieving high compression.

The performance of the proposed algorithm has showed superiority in all tests over the existing wavelets even with high detailed images like circulatory system images, from PSNR point of view. PSNR and CR values were increased for horizontal view for the CT (brain image) and MRI image (posterior cruciate ligament), respectively. Compressing X-ray (chest view) overcame best existing methods by six times.

The PSNR value is enhanced, when applied the proposed algorithm only on the detailed subbands. That can give greater flexibility towards our target either to gain more cleared image (high PSNR value) or saving more space (high CR value).

Future research, it is possible to integrate intelligence techniques with the proposed algorithm to create a learning dictionary that accelerates and helps in the process of compressing images of a convergent nature, which may lead to continuous improvement of the values of image compression, purity and speed up the process as a whole.