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Lossless Compression
Published in Jerry D. Gibson, The Communications Handbook, 2018
The idea behind entropy coding is very simple: use shorter codes for more frequently occurring symbols (or sets of symbols). This idea has been around for a long time and was used by Samuel Morse in the development of Morse code. As the codes generated are of variable length, it is essential that a sequence of codewords be decoded to a unique sequence of symbols. One way of guaranteeing this is to make sure that no codeword is a prefix of another code. This is called the prefix condition, and codes that satisfy this condition are called prefix codes. The prefix condition, while sufficient, is not necessary for unique decoding. However, it can be shown that given any uniquely decodable code that is not a prefix code, we can always find a prefix code that performs at least as well in terms of compression. Because prefix codes are also easier to decode, most of the work on lossless coding has dealt with prefix codes.
Video Compression
Published in Keshab K. Parhi, Takao Nishitani, Digital Signal Processing for Multimedia Systems, 2018
where pi is the probability of the ith symbol. The entropy of a source has the unit bits per symbol, or bits/symbol, and it is lower bounded by the average codeword length required to represent the source symbols. This lower bound can be achieved if the codeword length for the ith symbol is chosen to be – log2pi bits, i.e., assigning shorter codewords for more probable symbols and longer codewords for less probable ones. Although – log2pi bits/symbol may not be practical since – log2pi may not be an integer number, the idea of variable length coding which represents more frequently occurred symbols by shorter codewords and less frequently occurred symbols by longer codewords can be applied to achieve data compression. The data compression schemes which use source data statistics to achieve close-to-entropy bits/symbol rate are referred to as entropy coding. Entropy coding is lossless, since the original data can be exactly reconstructed from the compressed data.
Image Compression
Published in Vipin Tyagi, Understanding Digital Image Processing, 2018
Huffman Coding is an entropy encoding technique that uses variable length coding to form a tree, known as a Huffman tree, based on the probability distribution of symbols. Let there be a source S with an alphabet of size n. The algorithm constructs the code word as follows:Initially, for each symbol in S, a leaf node is created containing the symbol and its probability (Fig. 10.3a).Then, two nodes with the smallest probabilities become siblings under a parent node, which is given a probability equal to the sum of its two children’s probabilities (Fig. 10.3b). Subsequently, the same combining operation is repeated on a new alphabet of size n-1, taking two nodes with the lowest probabilities, and ignoring nodes that are already children.The process is repeated until a root node is reached (Fig. 10.3c).A code word is generated by labeling the two branches from every non- leaf node as 0 and 1. To get the code for each symbol, the tree is traversed starting from the root to the leaf nodes (Table 10.1).
An image compression approach for efficient pneumonia recognition
Published in The Imaging Science Journal, 2023
Sabrina Nefoussi, Abdenour Amamra, Idir Amine Amarouche
The image intensities vector x ∈ RN is transformed into the code space by the encoder using parametric analysis transform ga. After that, using the quantization function Q, we generate a discrete value vector y^ by processing the representation y. Afterward, the bitstreams are generated using entropy coding methods (like arithmetic coding [30]) to losslessly compress y^. Entropy coding [29] is used to exploit the statistical redundancy in that bitstream and reduce its length. Since integer rounding is a fundamentally non-differentiable function, during the training, the latent features quantization is approximately modelled by adding a uniform noise U (0.5, 0.5) to generate noisy codes y˜. To simplify, we use y^ to denote both the latent features with uniform noise added during training y˜ and the discretely quantized latent features during testing y^. On the other side, the reverse operations are applied on the received bitstreams; entropy decoding into the quantized representation y^. After that, it is transformed back to the image space x^ by a decoder using a parametric synthesis transform gs.
An image compression model via adaptive vector quantization: hybrid optimization algorithm
Published in The Imaging Science Journal, 2020
Pratibha Pramod Chavan, B. Sheela Rani, M. Murugan, Pramod Chavan
Lossy and lossless compression approaches both compressed the images via minimizing the image redundancy using several fundamental approaches listed below. (1) Minimize pixel correlation: The correlation among one pixel and its neighbors might be extremely strong [7]. Researchers may use variable length coding theory and statistical features to lower the quantity of storage after the correlation between the pixels is minimized. (2) Quantization: Quantization decreases the storage quantity by mapping larger values to a simple quantum value. Moreover, the quantization is a lossy procedure that causes irreversible deformation. (3) entropy coding is to reduce the image size for storage purposes [8,9]. According to the probability of the symbols, entropy coding provides codewords to the appropriate symbols. For decreasing the duplication, traditional image encoding formats including such JPEG, HEVC intra-frame encoding, and JPEG2000are used a pre-defined handmade transform, like DCT or DWT. After that, entropy coding and quantization are conducted to get a condensed bit stream [10,11].
An improved Huffman coding with encryption for Radio Data System (RDS) for smart transportation
Published in Enterprise Information Systems, 2018
C. H. Wu, Kuo-Kun Tseng, C. K. Ng, G. T. S. Ho, Fu-Fu Zeng, Y. K. Tse
The Huffman coding algorithm (Jakimoski and Subbalakshmi 2008), which was raised by Dr Huffman, is an entropy encoding algorithm based on the variable word length coding theory for lossless data compression. In the process of Huffman coding, each character is encoded with different lengths. In the Huffman coding, it receives the statistical information and then encodes the symbols corresponding to their statistical characters. In the process of encoding, there is only one principle to be followed: the character with a high frequency will be assigned a shorter code word and the low-frequency character with a longer code word.