Digital image compression of medical images in DICOM and in other formats is important in healthcare informatics owing to the pixel wise reproduction of the original image without any loss in the quality, for ease in storage and communication. Lossless compression plays a key role in medical imaging as it move towards complete film-less imaging and in tele-radiology. Though high compression ratio is in lossy compression techniques, the medical society is unwilling to adopt these methods owing to clinical relevance. In general lossless compression is widely used in clinically relevant regions and lossy compression is used in some imaging applications. High level compression ratio is very much in need for teleradiology applications, especially when there is a limitation in transmission and bandwidth, The objective is to have high compression ratio and by also maintaining the clinical relevance of information.
ADAPTIVE BINARY OPTIMIZATION (ABO)
The objective of ABO applied radiologic image compression is to reduce the data volume of and to achieve a low bit rate in the digital representation of radiologic images without any perceived loss of image quality. ABO™ is a feature-rich technology that delivers high data compression rates and security by a method of Repetition and Correlation Coding (RCC). In this process a byte-matrix and bit-matrix is constructed and further re-represented or re-ordered without adding or removing any values. This re-ordering generates repetitions that can be represented intelligently in bits rather than bytes. The ABO saturation curve for compression is more prolonged than other methods, thus ensuring better compression ratios. This task is accomplished using a logical operation and no complex mathematical operations. Similarly, the decompression task requires only the same type of simple operations.
Key features
• A core compression technology of lossless method by encoding medical images to a
mathematically lossless quality.
• Compared with traditional systems ABO does not depend on the elimination of data to achieve better compression.
• A feature-rich technology that delivers high data compression rates and security by the
Repetition and Correlation Coding (RCC) method, whereby a byte-matrix and a bit-matrix is constructed and
further re-represented or re-ordered without adding or removing any values.
• Thereby repetitions are represented in bits rather than bytes increase the data security.
• Saturation curve for compression is prolonged further compared with conventional methods, thus better
compression ratios ensured.
• Employs logical operations and simple mathematical process than that of the complicated mathematical
operations thereby increases the efficiency of compression time.
• Decompression requires the same simple operations with high degree of accuracy.
• ABO is very a light computational algorithm implies low load on CPU and low usage power consumption
• A platform technology is evolved from the core ABO to address various medical image standards such as
DICOM, JPG, TIFF etc.
• ABO generates substantial savings in:
o Storage Space
o Process time
o Transmission
• Advantages in Healthcare Informatics
o Improved Turn around times
o Increased Storage savings
o Substantial Bandwidth savings
o Enhanced User Experience through clinical relevance
The schematic represents the basic blocks of a typical simple compression scheme
In the transformation stage delimiters will be placed at appropriate places to make sure the modeling stage predicts the data size correctly. Next stage of modeling of data, higher compression can be achieved if the nature of the input stream was predicted i.e., when compressing the input stream, all previously encoded data can be used to predict the next symbol in the stream with a sufficient level of accuracy. Data Compression is otherwise called Source Coding. The upper limits of what source coders can achieve is defined theoretically the ‘Entropy’, which is an estimate of the redundancy in the data, or in other words the information content in the data. Entropy is the minimum number of bytes required to code a symbol. Most source coders work on the statistics gathered from the available data. In the simplest form it is assumed that more probable symbols (redundant data) require lesser bytes. It is defined as –p*log 2 (p), where ‘p’ is the probability of a symbol. Since the probability values range from 0 – 1, higher probable symbols mean values closer to 1. The logarithm of 1 for any base number system is 0. Thus higher probable symbols will require fewer bytes. The source coder can be considered to be a system, whose inputs are the data stream and its statistics; the output of the system is a sequence of bits (compressed bitstream) based on the statistics, from which the original data sequence can be reconstructed. Encoding and Decoding are terms that are commonly associated with the forward and reverse process of such a system.
PRINCIPLE OF ABOTM
ABO is architectured on the Repetition and Correlation Coding (RCC): a simple and effective data transformation algorithm with encryption and
REPETITION AND CORRELATION CODING
At the heart of ABO, lies a transformation called Repetition and Correlation Coding (RCC). In general, there is a certain degree of correlation in images. In data compression terminology we could loosely term the highly correlated images as low entropy images. RCC is an algorithm that is built to exploit this correlation and transform that data in such a way that traditional modeling and source coding schemes can achieve very good compression. RCC compares the surrounding pixels in an image, either horizontally or vertically, and stores the result of the comparison in two entities called the bit-matrix and the byte-matrix. The comparison is as follows,
Let Pxi,j be any pixel in the image, in the ith and jth column.
Let Pxi,j+1 be the pixel to be compared.
The comparison is written as
Pxi,j == Pxi,j+1 + where ∆ is the error estimate between the pixels.
On successful comparison, i.e. if the two pixels are correlated then the bit-matrix gets updated appropriately and the byte–matrix remains unchanged. This ensures that the byte–matrix gets updated only when there is no correlation. This in turn reduces the size of the data and also increases redundancy. The bit–matrix retains the inherent shapes and objects of the image and also is compressible at the same time. The error estimate ‘∆’, can be calculated locally for a set of pixels, globally for the whole image or adaptively based on the image. The error estimate is usually zero for highly correlated data. For the sake of understanding and simplicity the process is explained in the illustration with an assumption of the error estimate as ‘0’.
The matrix shown in the illustration above is taken from a typical highly correlated image. The RCC is applied in raster order (left to right and top to bottom). For every repetition a ‘1’ is registered in the bit-matrix, leaving the byte-matrix unchanged. If there is norepetition a ‘0’ is registered in the bit-matrix and the corresponding pixel value gets stored in the byte-matrix. For example, the second and the third pixels (both of value 150) are compared. Since the pixels are same, no entry is made in the byte–matrix to signify that there has been a repetition and the bit–matrix is updated with ‘1’. For the pixels 3 and 4, a ‘0’ is registered in the bit-matrix since they are not equal and the corresponding pixel value is registered in the byte-matrix. This process is repeated for the entire matrix.
The reverse of this process (decompression) is straightforward. When a ‘0’ is encountered from the bit–matrix, the pixel value is restored from the byte–matrix to the reconstructed matrix. This process is repeated till we get a change in the bit-matrix level. Now the current pixel value is repeated in the reconstructed matrix till we encounter the next change in the bit-matrix. This process gets repeated till we reconstruct the whole image.
ABO AND COMPRESSIBILITY
Information Theory States that a series of numbers is random if the smallest algorithm capable of specifying it to a computer has about the same number of bits of information as the series itself. Moreover it states that any random data cannot be further compressed. A corollary, in essence, to this is the limit posed by Shannon’s theory. ABO’s claim is that inducing repetitions by optimized re-arrangement increases the compressibility. Shannon’s Limit as such is not violated. Shannon’s limit is defined for data at source ‘as is’ without any changes. The entropy limit defined in such a condition is what Shannon’s theorem states. ABO technology conveys that once the data is re-represented or re-ordered (without adding any new information), new limits are set for better compression of such data. This re-ordering brings about repetitions which can be represented in bits intelligently than bytes. It is agreed that this also has a saturation point in how much it can be compressed and it is at this point the data will start to expand than compress. But the saturation limit is further extended than other methods thus ensuring more compression.
Since we are dealing in the spatial domain and the computations involved in such a re-ordering is very less. The price to pay is relatively less than other spatial domain methods or frequency domain methods (see Spatial Domain Vs Frequency Domain).
Let’s take the example of a logarithmic book with all the log values. On the first instance, we perceive (considering that you don’t know it is a log book) the data to be very random. By understanding the data representation and its inherent principle conveyed by the Log Formula, the data can be represented by a single equation. Taking the essence of this example to ABO, we say that by re-representing data (hence introducing repetitions) we have new contexts. Hence a data specific context based modeling suited to such data followed by adaptive source coding can deliver higher compression ratios.
COMPARISON OF ABO VERSUS RLE
In the following section let us take a small example of a data sequence containing the value ‘10’, 20 times. We will use this as an example to illustrate how ABO is different from others.
If the above sequence is coded using Run Length Coding (RLE),
This is a straight forward example for RLE, but this is rare in real scenario. Let’s consider this for briefness and explore the same with another sequence.
10 10 10 10 9 10 10 11 10 …………..10 10 10 10 10 10 (20 symbols)
Applying RLE, the sequence is not compressed much. Now let’s show how ABO will perform and differentiate between the two.
ABO results in 5 bytes of data (Byte-Matrix) and a Bit-Matrix equal to the size of the sequence. The data sequence of size 20 Bytes is reduced to 7.5 Bytes, whereas RLE method only reduces it to 10 Bytes. This method followed by Adaptive Modeling schemes and source coding techniques will further reduce the final compressed size.
Overall Comparison of ABO with other Available Technologies
Scenario with Ultrasound Image
Scenario with Other Modalities
THE DRIVING POINT
The term “Adaptive Binary Optimization (ABO)” was coined to reflect it’s capability to represent data in binary format as opposed to in Bytes. Energy compaction of any information can achieve its maximum only if the ground-level data representation is exploited well. This is what ABO does exactly. By introducing repetitions and representing information in bits, the technology is able to compact more information even before it is given as input to the source coder. In reality, excellent compactness statistics and lossless data transference are merely addendums to ABO’s growing repertoire of achievements.
Contrary to the notion till date that ABO is a data compression method, it should be emphasized that ABO is a data representation method that also works well for data compression. By introducing repetitions, we are re-introducing redundancy and thereby aiding compression.
While transformation is one step of the compression scheme, modeling and source coding based on the transformed data plays a very important role. Intelligence in adaptively modeling the transformed data is a factor not comprehended by people at large. Transformation to the frequency domain and subsequent modeling techniques are very large in number. But in many cases, content modeling of transformed data becomes more of a complex mathematical manipulation. By transforming data within the spatial domain, intelligent data modeling becomes more of understanding the essence of the transformed data and creating models for the same. This step is powered further by the unique repetition rendered by the transformation. These repetitions bring about different and unique contexts for different data. By having intelligent classifiers, modeling of such content empowers the source coders to deliver more compression. |
