Yirong Yang

## Introduction

Computed tomography (CT) is a medical x-ray imaging modality. New x-ray detectors capture spectral information that enables tissues in the body to be virtually decomposed into “basis materials” such as soft tissue, bone, and iodine (contrast agent) and are being considered for clinical CT systems.

In addition to the increased number of images, these images may also be of higher resolution. Together, in practice, the amount of data for transmission and storage may be greatly increased. Therefore, image compression without impacting image quality is highly desired.

Besides the general image compression principles, the material decomposition images are known to have negatively correlated noise between them and often share common features such as edges. Compression methods can use correlations between basis material images to reduce the number of bits needed to represent the material decomposition images.

Our goal is a lightwight lossless compression scheme for material decomposition images. Moreover, previous study shows that while maintaining diagnostic accuracy, lossy compression in medical imaging can also be clinically used. In particular, the material decomposition images can be combined retrospectively to produce a variety of other images, for example, virtual monoenergetic images. Errors due to lossy compression will propagate through to the new images, so a metric is needed for the errors in the material decomposition images as well as the new images. We will explore the limits of lossless compression, as well as the impact of lossy compression.

## Method

A general approach to image compression is to predict the sample value with a predictor that can be employed at both ends of the transmission, and to encode and transmit the prediction error instead of the original sample value. Our compression method is divided into two prats: prediction and encoding.

### Predictor

In practice, we would like to store and transmit a pair of water and iodine image sequences. They share common structures such as edges and have negatively correlated noise in each slice. But because of the nonlinear process in material decomposition and image reconstruction, it is hard to make a good prediction with a simple linear predictor.

Our prediction of x_{i}, a pixel sample in iodine image, is a function of pixel samples of a 3 – by – 3 patch in water image at the same location. We use a three layers feedforward network and randomly select 50000 samples as training data to learn the relationship between water image and iodine image.

### Encoder

#### Lossless compression – FLIF

Our prediction residuals are encoded with free lossless file format (FLIF), which is a novel lossless image format outperforms PNG, lossless WebP, lossless BPG, lossless JPEG2000, and lossless JPEG XR in compression ratios.

FLIF uses “meta-adaptive near-zeros integer arithmetic coding” (MANIAC) as entropy encoding method for compression, which is a variant of context-adaptive binary arithmetic coding (CABAC). They use a decision tree to dynamically learn the context model during encoding time.

FLIF supports Adam \infty interlacing, which enables progressive reconstruction of a compressed image. In each interlacing step, the number of rows or columns doubles. At decode time, the reconstructed image in each step is a lossy compression of the original image.

#### Lossy compression – JPEG 2000

Lossy compression could be considered in medical imaging if a compression ratio beyond the limit of lossless compression is needed. Different radiologists committees have accepted the principle of lossy compression for use in primary diagnosis and clinic review and announced the wavelet-based Joint Photographic Experts Group (JPEG) 2000 as one of the standard.

JPEG 2000 uses a discrete wavelet transform (DWT), which concentrates the image information in a small area and enables multi-resolution image representation. JPEG 2000 supports pixel precision of up to 16 bits and images larger than 64000 pixels, which is one of the advantages of JPEG 2000 over the other compression algorithms in medical image compression.

Also, several studies figured out that images compressed with JPEG 2000 at low compression ratios have better visual quality than original image, since the first level of decomposition in wavelet compression eliminates noises in the original image.

### Noise propagation

In practice, the material decomposition images can be combined retrospectively to produce a variety of other images, for example, virtual monoenergetic images and images of different virtual iodine levels. Errors due to lossy compression will propagate through to the new images, so a metric for the errors in the new images is also needed.

## Result

We use image data from 4 patient to test compressor performance.

To test the performance of the predictor, we encoded the original iodine image sequence and prediction residual image sequence in PNG, and compare their file sizes. Then, we transform the PNG files to FLIF, and evaluate the limit of lossless compression.

For lossy compression, we examined the image quality vs compression ratio to figure out the best compression ratio. In medical imaging, we originally store the images in integers. So, the compressed images are virtually lossless if the RMSE distortion between the original images and them is less than 1 pixel unit. And the compressed images are acceptable if the RMSE distortion between the original images and them is less than the level of standard deviation.

Further, with different lossy compression standards, we would like to analyze the image quality of virtual monoenergetic images, which is crucial in clinical systems.

We can observe that our feedforward network predictor has an average 2.62% improvement over PNG and an average 2.26% improvement over FLIF. And FLIF files are on average 34.16% smaller than PNG files.

For lossy compression using JPEG 2000 compressor, we could observe that when the compression ratio is 4.75, the compressed water image is virtually lossless, and the compression ratio for a corresponding virtually lossless iodine image could be 10. While for an acceptable lossy water image, the compression ratio could reach 7, and in this case, the compression ratio for a virtually lossless iodine image is 9.25.

With these compression parameters, we examine the file size and visual quality of lossy compression images of water and iodine.

We could observe that lossy compression further increases the compression ratio while maintaining the diagnostic accuracy.

We then fixed the compression ratio pairs ( *water 7, iodine 9.25; water 4.75, iodine 10* ) and analyzed the RMSE distortion between virtual monoenergetic images generalized from original images and lossy compressed images as a function of photon energy.

We could observe that although the lossy compression images of single material are virtually lossless or acceptable respectively, the generated virtual monoenergetic images suffers from increased RMSE distortion compared with basis material images. While the virtual monoenergetic images are weighted linear combination of the basis material images, the distortion will also be added up. And this distortion is increasing while the photon energy is decreasing, since the weighted combination factors (attenuation coefficients) increase while the energy is decreasing.

## Conclusion and further work

In conclusion, we have designed a simple predictor to capture the relationship between material decomposition images, which gives an average of 2.62% improvement over PNG and an average of 2.26% improvement over FLIF. We also investigate the error in lossy compression as a function of compression ratio, and figured out the “acceptable” compression parameters for single material images. We further test the noise propagation effect in generating virtual monoenergetic images.

Further work includes better predictors that takes advantage of the nonlinear relationships between the basis material images, such as the anatomy, material decomposition algorithm and image reconstruction process to achieve higher compression ratio in lossless compression. For lossy compression, further work will focus on optimal basis materials to use for storage, as well as worst-case materials to recover from the stored basis materials.

## Reference

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