Computerized
Printed
Medical Imaging and Graphics.
in the USA.
Vol.
IS.
No. 4. pp. 217-283.
1991 Copyright
All rights reserved.
0895.6llEJl $3.00 + .OO 0 1991 Pergamon Press plc
INFORMATION PRESERVING IMAGE COMPRESSION FOR ARCHIVING NMR IMAGES C.C. Li, M. Gokmen, Department
of Electrical Engineering,
A.D. Hirschman* University
and Y. Wang**
of Pittsburgh,
Pittsburgh,
PA 15261 USA
(Received 14 December 1990)
Abstract-This paper presents a result on information preserving compression of NMR images for the archiving purpose. Roth Lynch-Davisson coding and linear predictive coding have been studied. For NMR images of 256 x 256 X 12 resolution, the Lynch-Davisson coding with a block size of 64 as applied to prediction error sequences in the Gray code bit planes of each image gave an average compression ratio of 2.3:1 for 14 testing images. The predictive coding with a third order linear predictor and the HuEman encoding of the prediction error gave an average compression ratio of 3.1:1 for 54 images under test, while the maximum compression ratio achieved was 3.&l. This result is one step further toward the improvement, albeit small, of the information preserving image compression for medical applications. Key Words: Image compression, Image archiving
Image coding, Information
INTRODUCTION
preserving,
Error free, NMR images,
Medical images,
able compression ratio depends on the image type, spatial resolution, intensity resolution, and histogram characteristic of the image. It has been reported (34) that the information preserving techniques such as Huffman coding and the run-length coding applied to bit planes of a radiological image may give an average compression ratio between 2: 1 to 3: 1. Elimination of the featureless region, for example, around a reconstruction circle in a CT image, can improve the compression ratio. The irreversible approach such as the 2-dimensional cosine-transform with full-frame bit allocation technique can achieve a high compression ratio between 1O:l to 25:l and yet yield a high quality reconstructed image without ,apparent degradation for visual diagnosis, as reported by Lo and Huang (5, 7-9). Nevertheless, there are always concerns that the clinically significant information must be surely retained for archiving medical images. The American College of Radiology and the National Electrical Manufacturers Association had a joint working group to consider this problem (10). In general, NMR images have high intensity resolution but low spatial resolution; the NMR imaging generates images with more contrast, and hence less correlation, than X-ray CT images. These factors make NMR images less compressible. Some recently developed efficient compression algorithms such as the conditional run-length and variable-length coding algorithms (11) are not applicable to archive NMR images; they require 2” x 2” states in a table codebook which is prohibitively large for NMR images (n= 12 bits per pixel). This paper is to present the result of our study
The increasing use of digitally formatted images in diagnostic radiology, including digital radiographs, CT, and NMR images, has motivated studies for an efficient means of storing these image data. On the one hand, optical disks have been used as storage media in a number of radiological centers; on the other hand, methods of encoding the image data are being critically examined in order to recommend an overall best image compression scheme or a few compatible schemes for archiving purpose. There are two distinct approaches for image compression: information preserving approach and irreversible approach (1, 2). The information preserving approach is the one which encodes an image by removing, or at least reducing, the redundancy in the data in such a way that the original image can be exactly reconstructed from the coded data. The irreversible or information reducing approach is the one whose encoding process will not keep all of the original information, but the reconstructed image retains the original image quality to a large degree. The compression ratio, which can be defined as the ratio of the average bits per symbol before compression to the average bits per symbol after compression, is considerably smaller for the information preserving techniques than that achievable by the irreversible techniques. The attain-
*Current address: MEDRAD, Inc., Coralyn Building, P.O. Box 730, Indianola, PA 15051. **Department of Radiology, VA Medical Center, University of Pennsylvania, Philadelphia, PA 19104. 277
Computerized
278
Medical Imaging and Graphics
on some information preserving image compression methods for archiving NMR images. APPLICATION OF LYNCH-DAVISSON CODING Lynch-Davisson coding is a universal coding whose performance is independent of the source statistics. In most cases, it is superior to the run-length encoding except for images with very small source entropy. It was originally developed for binary memoryless sources (1). To apply the Lynch-Davisson coding to gray level images, it is required to transform each image into a binary memory-less source. This can be accomplished by means of bit planes or some modifications which will be discussed later. Let us first briefly review the idea of Lynch-Davisson coding. Lynch-Davisson coding algorithm The Lynch-Davisson coding of patterns of binary se-
quences of length N is based on the ranking of the sequences by using Pascal triangle rules. Before ranking, a given sequence is converted into an equivalent but less correlated pattern by representing a nonredundant sample by a “ 1” and a redundant sample by a “0”. An integer T representing the rank of the sequence and an integer q denoting the number of nonredundant samples in the sequence are used to encode the pattern. T is given by
where nj is the sample number of the jth nonredundant sample, 1snjlN1, 1Sj’q (if qZ l), and OSq5N - 1. T is unique for each pattern of q nonredundant samples distributed over N- 1 positions and can be obtained from a look-up table. The Lynch-Davisson code for the sequence is then given by (q,T) represented in a binary form. The number of bits required for q and T are, respectively
Kq =
and K, =
Printed
Medical Imaging and Graphics.
in the USA.
Vol.
IS.
No. 4. pp. 217-283.
1991 Copyright
All rights reserved.
0895.6llEJl $3.00 + .OO 0 1991 Pergamon Press plc
INFORMATION PRESERVING IMAGE COMPRESSION FOR ARCHIVING NMR IMAGES C.C. Li, M. Gokmen, Department
of Electrical Engineering,
A.D. Hirschman* University
and Y. Wang**
of Pittsburgh,
Pittsburgh,
PA 15261 USA
(Received 14 December 1990)
Abstract-This paper presents a result on information preserving compression of NMR images for the archiving purpose. Roth Lynch-Davisson coding and linear predictive coding have been studied. For NMR images of 256 x 256 X 12 resolution, the Lynch-Davisson coding with a block size of 64 as applied to prediction error sequences in the Gray code bit planes of each image gave an average compression ratio of 2.3:1 for 14 testing images. The predictive coding with a third order linear predictor and the HuEman encoding of the prediction error gave an average compression ratio of 3.1:1 for 54 images under test, while the maximum compression ratio achieved was 3.&l. This result is one step further toward the improvement, albeit small, of the information preserving image compression for medical applications. Key Words: Image compression, Image archiving
Image coding, Information
INTRODUCTION
preserving,
Error free, NMR images,
Medical images,
able compression ratio depends on the image type, spatial resolution, intensity resolution, and histogram characteristic of the image. It has been reported (34) that the information preserving techniques such as Huffman coding and the run-length coding applied to bit planes of a radiological image may give an average compression ratio between 2: 1 to 3: 1. Elimination of the featureless region, for example, around a reconstruction circle in a CT image, can improve the compression ratio. The irreversible approach such as the 2-dimensional cosine-transform with full-frame bit allocation technique can achieve a high compression ratio between 1O:l to 25:l and yet yield a high quality reconstructed image without ,apparent degradation for visual diagnosis, as reported by Lo and Huang (5, 7-9). Nevertheless, there are always concerns that the clinically significant information must be surely retained for archiving medical images. The American College of Radiology and the National Electrical Manufacturers Association had a joint working group to consider this problem (10). In general, NMR images have high intensity resolution but low spatial resolution; the NMR imaging generates images with more contrast, and hence less correlation, than X-ray CT images. These factors make NMR images less compressible. Some recently developed efficient compression algorithms such as the conditional run-length and variable-length coding algorithms (11) are not applicable to archive NMR images; they require 2” x 2” states in a table codebook which is prohibitively large for NMR images (n= 12 bits per pixel). This paper is to present the result of our study
The increasing use of digitally formatted images in diagnostic radiology, including digital radiographs, CT, and NMR images, has motivated studies for an efficient means of storing these image data. On the one hand, optical disks have been used as storage media in a number of radiological centers; on the other hand, methods of encoding the image data are being critically examined in order to recommend an overall best image compression scheme or a few compatible schemes for archiving purpose. There are two distinct approaches for image compression: information preserving approach and irreversible approach (1, 2). The information preserving approach is the one which encodes an image by removing, or at least reducing, the redundancy in the data in such a way that the original image can be exactly reconstructed from the coded data. The irreversible or information reducing approach is the one whose encoding process will not keep all of the original information, but the reconstructed image retains the original image quality to a large degree. The compression ratio, which can be defined as the ratio of the average bits per symbol before compression to the average bits per symbol after compression, is considerably smaller for the information preserving techniques than that achievable by the irreversible techniques. The attain-
*Current address: MEDRAD, Inc., Coralyn Building, P.O. Box 730, Indianola, PA 15051. **Department of Radiology, VA Medical Center, University of Pennsylvania, Philadelphia, PA 19104. 277
Computerized
278
Medical Imaging and Graphics
on some information preserving image compression methods for archiving NMR images. APPLICATION OF LYNCH-DAVISSON CODING Lynch-Davisson coding is a universal coding whose performance is independent of the source statistics. In most cases, it is superior to the run-length encoding except for images with very small source entropy. It was originally developed for binary memoryless sources (1). To apply the Lynch-Davisson coding to gray level images, it is required to transform each image into a binary memory-less source. This can be accomplished by means of bit planes or some modifications which will be discussed later. Let us first briefly review the idea of Lynch-Davisson coding. Lynch-Davisson coding algorithm The Lynch-Davisson coding of patterns of binary se-
quences of length N is based on the ranking of the sequences by using Pascal triangle rules. Before ranking, a given sequence is converted into an equivalent but less correlated pattern by representing a nonredundant sample by a “ 1” and a redundant sample by a “0”. An integer T representing the rank of the sequence and an integer q denoting the number of nonredundant samples in the sequence are used to encode the pattern. T is given by
where nj is the sample number of the jth nonredundant sample, 1snjlN1, 1Sj’q (if qZ l), and OSq5N - 1. T is unique for each pattern of q nonredundant samples distributed over N- 1 positions and can be obtained from a look-up table. The Lynch-Davisson code for the sequence is then given by (q,T) represented in a binary form. The number of bits required for q and T are, respectively
Kq =
and K, =
