Application of SPIHT algorithm in lossless compression of medical images

1 Introduction

With the development of society and the advancement of medical technology, people are more and more concerned about their health. Medical images are no longer just information for doctors to refer to, but have become an important basis for diagnosing diseases. Image compression coding under network transmission conditions has become a key technology for establishing digital hospitals. At present, the compression standards for two-dimensional images include JPEG, GIF, and JPEG2000 using wavelet transform. Medical images are special and generally do not allow the loss of useful detail information. Traditional DCT (Discrete Cosine Transform) and the first generation of wavelets will produce floating point numbers after image transformation, so the transformed data must be quantized, which will produce different degrees of distortion. It can be seen that the design of the quantizer is a key link in determining the fidelity of the image. Since the second generation of wavelets can achieve integer transformation using the lifting method, it can achieve lossless compression of images. Obviously, it is a very suitable compression method for medical images.

2 SPIHT algorithm

The Set Partitioning in Hierarchical Trees (SPIHT) algorithm improves the Embedded Zerotree Coding (EZW) algorithm. After the image is wavelet transformed, it more effectively utilizes the similarity between the important coefficients of subbands of different scales. It exhibits good characteristics: it constructs wavelets in the spatial domain without relying on Fourier transform; the high PSNR (Peak Signal Noise Ratio) ensures good image reproduction quality; integer operations are conducive to real-time fast encoding and decoding and network transmission; the gradual presentation of the image code stream makes it easier for users to search for images of interest online.

The SPIHT algorithm uses the following encoding steps for image information.

First, three queues are defined: the insignificant coefficient queue LIP, the significant coefficient queue LSP and the insignificant set queue LIS.

Assume that O(i, j) represents the set of direct nodes of node (i, j); D(i, j) represents the set of child nodes of node (i, j); and L(i, j) represents the set of child nodes excluding direct nodes.

In the queue, each element is uniquely identified by a coordinate, which represents the isolation coefficient (the root node without children) in LIP and LSP, and D(i, j) for the first-class elements or L(i, j) for the second-class elements in LIS.

Perform a significance test on a certain threshold T. Move elements greater than T into the LSP and remove them from the LIP queue. Perform the same test on the LIS, move the significant elements into the LSP, and split the others.

The SPIHT algorithm described in C++-like language is as follows:

In the first step, the threshold T and three queues (LSP, LIS and LIP) are initialized.

(2) If (x, y) is a second-category element, perform a significance test on L(i, j)

if (L(i, j)) == 1 all(k, l)∈O(i, j) are moved into LIS as first-class elements and dequeued from LIS.

The third step is bit transmission/storage. Each coefficient in the LSP is converted into binary for transmission/storage.

Step 4: Update the threshold and go to step 2: T/=2; gotostep2.

3 Lifting Scheme and Second Generation Wavelet

The construction of wavelet by lifting method is divided into three steps: splitting, prediction and updating.

3.1 Split

An original signal sequence Sj is divided into two smaller, non-intersecting wavelet subsets Sj-1 and dj-1 according to even and odd numbers:

3.2 Prediction

Since there is correlation between data, we can define a prediction operator P so that dj-1=P(Sj-1), so that the adjacent even-numbered sequence can be used to predict the odd-numbered sequence. If the difference between dj-1 and P(Sj-1) is used to replace dj-1, the amount of data is much smaller than the original dj-1.

In the simplest case, the mean of the data of two adjacent even-numbered sequences is taken as the predicted value of the data of the odd-numbered sequence between them. That is,

3.3 Update

Since the above two processes generally cannot maintain some overall properties of the original image (such as brightness), we need to construct a U operator to update Sj-1 so that it maintains some characteristics of the original data set

.

In this paper, the front end uses the second generation wavelet (lifting wavelet), then uses the SPIHT algorithm for the wavelet coefficients, and then uses Amir Said's adaptive arithmetic coding. Decoding is the inverse process of encoding, including three steps corresponding to the forward SPIHT: recovery update, recovery prediction and merge. The encoding/decoding scheme is shown in Figure 1.

If the front end uses the first generation wavelet for lossy compression, a higher compression ratio can be achieved. Obviously, the second generation wavelet transform's requirements for high fidelity and high compression ratio for data compression are contradictory.

5 Experimental results and conclusions

For the above coding scheme, we tested medical images and Lena images respectively, and the bit rate bbp was bit/pixel. Since the lossless compression scheme was adopted, the three different coding methods in Table 1 all have PSNR=∞.

As can be seen from Table 1, the performance difference is not very large when encoding the standard test image Lena, but since there are a large number of "zero pixels" at the edges of general medical images, a large number of "zero trees" can be generated when using SPIHT encoding, which greatly reduces the amount of data. Therefore, when compressing medical images, it is more suitable to use the method in this paper.

Further analysis shows that compared with the currently widely used JPEG, this compression scheme occupies less memory, has high coding efficiency and no mosaic phenomenon. At low bit rates, the difference between the two is more obvious. If the scheme adopts parallel fast algorithms and hardware implementation, its real-time performance will be further improved. Therefore, this medical image compression scheme has good application prospects.