^{1}

^{*}

^{1}

^{1}

^{2}

This paper presents a medical image compression approach. In this approach, first the image is preprocessed by Differential Pulse Code Modulator (DPCM), second, the output of the DPCM is wavelet transformed, and finally the Huffman encoding is applied to the resulting coefficients. Therefore, this approach provides theoretically threefold compression. Simulation results are presented to compare the performance of the proposed (DPCM-DWT-Huffman) approach with the performances of the Huffman incorporating DPCM (DPCM-Huffman), the DWT-Huffman and the Huffman encoding alone. Several quantitative indexes are computed to measure the performance of the four algorisms. The results show that the DPCM-DWT-Huffman, the DWT-Huffman, the DPCM-Huffman and the Huffman algorisms provide compression ratio (CR) of 6.4837, 4.32, 2.2751 and 1.235, respectively. The results also confirm that while the proposed DPCM-DWT-Huffman approach enhances the CR, it does not deteriorate other performance quantitative measures in comparison with the DWT-Huffman, the DPCM-Huffman and the Huffman algorisms.

The main objective of image compression techniques is to reduce the image size for less storage and transmission bandwidth by discarding irrelevance and redundancy of the image data. These techniques can be classified into two categories: lossless and lossy compression techniques. Lossless techniques are applied when data are critical and loss of information is not acceptable. Hence, many medical images should be compressed by lossless techniques [

An efficient compression method for medical images is proposed. The method is based on adding a data size reduction to the DPCM output prior to Huffman encoding. This is done by discreet wavelet transformation (DWT). The DWT is an efficient method to represent data with fewer numbers of coefficients. Then, the expected compression can be threefold. Comparison between the proposed method and other ones to measure the performance has been applied. Other methods have been explained in details in next section. The paper is organized as follows. In Section 2, the main idea of Huffman encoding is presented. The DPCM-Huffman method is discussed in Section 3. In Section 4, The DWT-Huffman is discussed. In Section 5, the proposed method of incorporating the DWT with the DPCM-Huffman compression method is discussed. Section 6 shows and discusses the compression results provided by the four techniques: Huffman, DPCM-Huffman, DWT-Huffman and the proposed DPCM-DWT-Huffman. Finally, Section 7 presents the conclusion.

1) More frequently occurred symbols will have shorter code words than symbol that occur less frequently;

2) The two symbols that occur least frequently will have the same length.

The average length of the code is given by the average of the product of probability of the symbol and number of bits used to encode it. More information can found in [

And the Huffman code efficiency is calculated as

Huffman’s procedure creates the optimal code for a set of symbols and probabilities subject to the constraint that the symbols be coded one at a time [

The entropy (H) of the source can be determined from the following Equation (2). The entropy value describes how much compression is possible for that image in the form of bit per pixel. It should be noted that, there cannot be any possible compression ratio smaller than entropy. The entropy of any image is calculated as the average information probability. Entropy indicates the required amount of bits per pixel [

where p_{k} is the probability of intensities, k is the intensity value, and L is the number of intensity values used to present image.

In [

Differential pulse code modulation (DPCM) is an operation of converting a signal into a predicted one. Then the differences between the original signal values and predicted ones are encoded and stored. DPCM compression method can be conducted for intra and inter frame coding. Intra coding exploits spatial redundancy and inter coding exploits temporal redundancy. In the intra-frame coding, is formed by the difference between the neighbouring pixels of the same frame, further, the inter-frame is formed between two consecutive frames for the same value. In both the value of target pixel is predicted by neighbouring pixels. DPCM compression depends on the prediction technique, which leads to good compression rates [

DPCM prediction is nonlinear. Its basic idea is to predict the value in every image pixel and make the predicted error entropy less than the original image entropy. Because there is strong correlation among adjacent pixels, current pixel values are predicted by knowledge of its adjacent pixels.

of an N-point sequence x [n], 0 ≤ n ≤ N − 1 is given by

where,

1) A lot of 1D wavelet design materials exist in the literature;

2) Fast implementation of 1D DWT is also available.

Here, the 2D discrete wavelet transform has been adopted for image compression. We will, therefore, focus our attention on the implementation of 2D DWT of an image using 1D DWT in a row-column fashion [

The HL coefficients correspond to highpass in the horizontal direction and lowpass in the vertical direction. Thus, the HL coefficients follow horizontal edges more than vertical edges. The LH coefficients follow vertical edges because they correspond to highpass in the vertical direction and low-pass in the horizontal direction. Finally, the HH coefficients preserve diagonal edges.

^{(h)}), LH (cD^{(v)}), and HH (cD^{(d)}) coefficients, the inverse 2D DWT is applied as shown in

representing the error signal. Then the Huffman encoding is applied to the nonzero coefficients. The wavelet family Haar of level one has been used.

To gain more compression we propose to incorporate the DWT within the DPCM-Huffman algorithm explained in Section 5 as shown in

senting data (signal or image) by approximation and detailed coefficients. In one level image analysis, the approximation wavelet coefficient shows the general direction of the pixel value, and three detailed coefficients shows vertical, horizontal and diagonal details. Compression ratio increases when the number of wavelet coefficients that are equal zeroes increases [

The DPCM has been carried out by studying all possible predictors and select the most efficiency one through the calculation of the entropy of each predictor and comparing between them, which found B is the best predictor. However, the prediction error (e), which is the difference between the actual value of the current pixel (X) and the predicted one (B) is given by the following equation.

Proposed method applies the wavelet transform to the prediction error generated by DPCM to obtain the approximation and detailed coefficients representing the error signal. Then, the Huffman encoding is applied to the nonzero coefficients and to reject other ones.

The most common objective performance measures used are Maximum Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR), Compression Ratio (CR). The error function between the reconstructed and original images is given by

where

The MSE is the second moment of the error function between the reconstructed and original images, given by [

where, M × N is the image size. The RMSE is simply the square root of the MSE given by (3).

The SNR in dB is given by

where the numerator is the power of the original image and denominator is the additive noise corrupting the reconstructed image. The PSNR measure the ratio the maximum pixel intensity

Therefore, a higher value of PSNR offers better performance. The CR is often computed by dividing the size of the original image in bits over the size of the compressed image data. Thus it is given by [

The three methods, Huffman, DPCM-Huffman and the proposed DPCM-DWT-Huffman, have been applied to three CT medical images with different sizes.

To show the rational of incorporating the wavelet transform between the DPCM and Huffman coding, we have executed the following simulation. For an exemplary image shown in

We have also applied the proposed DPCM-DWT-Huffman on different medical images shown in Figures 10-12 which selected from U.S. National Library of Medicine (NLM) [

Methods | Metrics | ||||
---|---|---|---|---|---|

SNR | MSE | RMSE | PSNR | CR | |

Huffman | Inf | 0.00 | 0.00 | Inf | 1.2351 |

DPCM + Huffman | 15.09 | 31.43 | 5.61 | 33.16 | 2.2751 |

DWT (haar) + Huffman | 11.80 | 61.63 | 7.85 | 30.23 | 4.3214 |

DPCM + DWT (db1) + Huffman | 10.60 | 85.48 | 9.25 | 28.81 | 6.4837 |

DPCM + DWT (db4) + Huffman | 11.85 | 63.96 | 8.00 | 30.07 | 5.3387 |

DPCM + DWT (Haar) + Huffman | 10.60 | 85.48 | 9.25 | 28.81 | 6.4837 |

Methods | Metrics | ||||
---|---|---|---|---|---|

SNR | MSE | RMSE | PSNR | CR | |

Huffman | Inf. | 0.00 | 0.00 | Inf. | 2.1291 |

DPCM + Huffman | 14.93 | 33.23 | 5.76 | 32.92 | 3.5604 |

DWT (haar) + Huffman | 20.30 | 9.11 | 3.02 | 38.54 | 7.4089 |

DPCM + DWT (db1) + Huffman | 14.23 | 62.09 | 7.88 | 30.20 | 11.591 |

DPCM + DWT (db4) + Huffman | 15.78 | 33.38 | 5.78 | 32.90 | 11.051 |

DPCM + DWT (Haar) + Huffman | 14.23 | 62.09 | 7.88 | 30.20 | 11.591 |

Methods | Metrics | ||||
---|---|---|---|---|---|

SNR | MSE | RMSE | PSNR | CR | |

Huffman | Inf | 0 | 0 | Inf | 1.6378 |

DPCM + Huffman | 19.41 | 9.91 | 3.15 | 38.17 | 5.7112 |

DWT (haar) + Huffman | 12.40 | 51.08 | 7.15 | 31.05 | 2.5313 |

DPCM + DWT (db1) + Huffman | 11.52 | 70.27 | 8.38 | 29.66 | 8.7130 |

DPCM + DWT (db4) + Huffman | 11.68 | 96.04 | 9.80 | 28.31 | 8.4573 |

DPCM + DWT (Haar) + Huffman | 11.38 | 98.59 | 9.93 | 28.19 | 8.7130 |

In this paper, we have presented a new image compression technique consisting of the association of the DPCM, the DWT and the Huffman coding. In this technique, first the image is passed through the DPCM transformation, second the wavelet transformation is applied to the DPCM output, and finally the wavelet coefficients are encoded by the Huffman coding. So, the wavelet transformation reduces the redundancy and spatial reputation in the image data, which makes the compression more efficiently. Simulation results have shown that the proposed DPCM-DWT-Huffman outperforms the DWT-Huffman, DPCM-Huffman and Huffman methods. The four methods provide CR of 6.48, 4.32, 2.27 and 1.2 respectively.