Digital video images are one of the most important information media, which are intuitive, vivid and rich in content. The most commonly used method to solve this problem is to perform digital image compression encoding, which minimizes the amount of image data while ensuring imag

Digital video images are one of the most important information media, which are intuitive, vivid and rich in connotation. However, due to the very large amount of data in digital images, it brings great difficulties to the storage, transmission and processing of images. The most commonly used method to solve this problem is to perform digital image compression encoding, which minimizes the amount of image data while ensuring image quality, so as to reduce the amount of data storage and save transmission and processing time. The mechanism by which

can perform image compression mainly comes from two aspects: First, there is a large amount of statistical redundancy (such as spectrum redundancy, spatial redundancy, time redundancy, etc.) in the image signal for compression. This redundancy can be restored without distortion after decoding; the second is to take advantage of the visual physiological redundancy of the human eye. For example, the human eye is not sensitive to high-frequency components of color and not sensitive to high-frequency components of brightness, and is not sensitive to noise at high frequencies (details) of the image. Sensitive, etc., by reducing the accuracy of the signal without being noticed by subjective vision, a certain objective distortion is exchanged for data compression.

The most basic image compression coding methods include statistical coding, predictive coding, and transform coding. Later, subband coding, fractal coding, wavelet transform coding, etc. appeared. Only an overview of these compression encoding techniques is provided here.

1. Statistical coding

Statistical coding is a compression coding based on the distribution characteristics of the probability of occurrence of pixel gray values, or a probability matching coding based on the different probability of occurrence of each signal source symbol. It can minimize the average code length required to transmit each source symbol without causing any distortion. Statistical encoding identifies the most frequent bit and byte patterns in a given code stream and encodes it using fewer bits than the original bits . That is, the lower the frequency of the mode, the more coding bits it has, and the higher the frequency mode has the fewer coding bits.

statistical encoding is lossless compression (ie, distortion-free compression) and can usually be divided into two major categories.

(1) pattern replacement. It is an encoding commonly used for text information. Replace characters that appear multiple times, that is, common words, with one character. For example, replace "Communication" with "C" and "Netwok" with "N".

(2) Huffman encoding. is a common statistical encoding. For a given data stream, calculate the frequency of occurrence of each byte. According to the frequency table , the Huffman algorithm can be used to determine the minimum number of digits assigned to each character, and then an optimal encoding is given, and the codeword is passed into the code book. Huffman coding is suitable for compressing both static and dynamic images. Depending on the parameters, a new codebook can be constructed for several images or a group of images. In moving images, the codebook can be recalculated for a frame or a series of frames. In all cases, the codebook must be transferred from the source to the target for decoding to occur. Its advantage is that it can well match the probability distribution of the coded symbols, so that the average code length can be minimized; but its hardware implementation is more complicated; the encoding requires knowing the statistical characteristics of the source, that is, the occurrence of each source symbol probability, otherwise the coding efficiency will be significantly reduced.

2. Differential or predictive coding

predictive coding is to use the pixels that have been encoded and transmitted to predict the actual pixels to be transmitted. That is, the predicted pixel value is subtracted from the actual pixel value to be transmitted, and their difference is transmitted, so it is also called differential coding. Obviously, transmitting the difference values ​​requires a lower bit rate than transmitting the original image values. Because there is a strong correlation between each pixel of the image, using predictive coding can reduce the correlation between pixels, improve transmission efficiency, and compress the bit rate. Differential encoding is particularly useful for signals whose consecutive values ​​differ greatly from zero but not significantly from each other. Therefore, the code is very suitable for moving picture signals (it only conveys the difference of the image) or audio signals. Predictive coding can be divided into lossless prediction and lossy prediction. In practice, various forecasting techniques differ due to different methods of determining forecast values.

differential encoding technology has three categories: DPCM, 6 modulation and ADPCM.DPCM (Differential Pulse Code Modulation) is a practical lossy predictive coding technology and the earliest digital image compression technology. Its principle is that the current pixel can be predicted from its neighboring pixel values, that is to say, its Redundancy can be determined from neighboring pixels. Accordingly, the difference between the current pixel and the predicted pixel is quantized and encoded. Considering the trade-off between high performance and complexity, the number of neighboring pixels usually used for intra prediction (2D prediction) is not large (no more than 4), and using more pixels cannot achieve Significant improvement in forecasting performance. For inter-frame prediction (3D prediction), generally only the corresponding pixels of adjacent frames are used for prediction. The greater the correlation of the image, the smaller the prediction error and the greater the compression ratio achieved. DPCM is a relatively easy compression method to implement, but its compression capability is generally not as good as the following transform coding at lower rates.

3. Transform coding

predictive coding directly compresses images in the spatial domain, while transform coding is equivalent to compression in the frequency domain. The basic principle of transform coding is to convert the image from the spatial domain to the transform domain with relatively concentrated energy through orthogonal functions, and then quantize and encode the transform coefficients to achieve the purpose of reducing the bit rate. Therefore, transformation coding is also called orthogonal transformation coding. For the coefficients in the transformation domain obtained by most natural image transformations, some values ​​are very small, and these coefficients can be quantized coarsely, or even completely ignored to produce only a small distortion. Although the distortion is very small, there is still a loss of information, so transform coding is a lossy compression coding method. Transform coding is a source coding method, and source coding takes into account the properties of the signal being compressed, in particular it depends on the characteristics of audio, still images and dynamic images. When

transforms the encoding, the initial data must be mathematically transformed from the initial space or time domain into an abstract domain more suitable for compression. The process is reversible, i.e. the original data can be recovered using the inverse transformation. In the transformation coding method, an optimal transformation must be selected to achieve optimal compression for specific data, and the nature of the data must be considered here. The idea is: after transformation, the most important parts of the information (that is, the most important coefficients containing the greatest "energy") are easily identifiable and may appear in groups. Transform coding is particularly suitable for image compression. A commonly used mathematical transformation is the discrete cosine transform (DCT).

4. Subband coding

subband coding uses the bandpass filter group to decompose the signal into the sum of components in several frequency bands, and moves each K band to zero through a modulation process equivalent to single sideband amplitude modulation. After obtaining a low-pass representation near the frequency, each sub-band is output sampled at the Nyquist rate , and the sampled values ​​are subjected to usual digital encoding. At the receiving end, each subband signal is decoded and re-modulated back to its original position, and then all subband outputs are added together to obtain a restored waveform close to the original signal.

divides the signal into sub-bands and then encodes it, which has the following advantages.

•Through frequency decomposition, signal frequency correlation can be removed and redundancy reduced.

• Due to the different distribution of energy in different frequency bands, codewords of different lengths can be used to encode signals in different frequency bands.

• Since quantization is performed separately in each sub-band, the quantization noise is limited to each sub-band, which can prevent signals in smaller energy bands from being interfered and affected by quantization noise in other frequency bands.

Practice has proved that under the same distortion conditions, sub-band encoding will have a lower bit rate than full-band encoding.

5. Fractal compression coding

The basic idea is that the traditional geometry of drawing straight lines and circles is not similar to the natural geometric shapes . A kind of geometry called fractal can be used to describe nature. In different locations, different ranges and different Under the angle, various irregular changes are repeated, and different appearances of the same fractal are depicted using so-called fractal transformations.

fractal image compression is to seek a set of fractals in an image, and reconstruct or describe the original entire image from this set of fractals.Once this set of fractals is found, the original image can be well restored by retaining only this set of fractals, thereby achieving the purpose of data compression. This is due to the characteristics of these fractals such as self-similarity and infinite scale changes. Therefore, the key to fractal image compression lies in finding this group of fractals, that is, the iterative function system (IFS) in the theoretical basis of fractal image compression. There are two methods to find IFS: one is to directly calculate the coefficients of each contraction affine transformation of the iterative function system based on the self-similarity of the image; the second is to divide the image into into smaller objects, and then obtain it from the iterative function system library Find the iterative function system corresponding to these small objects.

fractal image compression is a new compression coding technology that uses the self-similarity of images to reduce image redundancy. Its advantages are as follows.

•has a very high compression ratio. For general images, when the compression ratio is more than 20 times, there is still good fidelity. For some images with strong self-similarity, the compression ratio can reach hundreds of times.

• The decoded image has nothing to do with the resolution. It can be decoded at any resolution higher or lower than the original image. When it is to be decoded into a high-resolution image, the details introduced will be roughly consistent with the entire image, which is better than pixel copying or Interpolation methods produce images that look more natural (this scaling capability can also be applied to image enhancement).

•The image decoding speed is fast, and the image reconstruction speed of several frames per second can be achieved by relying on special hardware. However, the image encoding time is too long and the real-time performance is poor, which hinders the practical application of this method.

6. Wavelet transform coding

Wavelet transform WT (Wavelet Transfonn) expands the signal into a sequence of basis function sets called wavelets. It is a new method of expressing signals that are limited in both the time domain and frequency domain. This transformation is very effective for spectrum analysis of transient signals within a small range. Since the multi-resolution characteristics of wavelet transform are very suitable for image compression, many interesting encoders can be produced. wavelet analysis brings new tools to digital image compression coding with its good local characteristics, making this field full of vitality. The image decomposition idea of ​​

wavelet is a special case of sub-band decomposition. It is a complete, orthogonal, and multi-resolution decomposition. In the spatial domain, wavelet decomposition decomposes the signal into different levels of decomposition operations and forms a multi-level decomposition in the frequency domain. At each level in frequency domain , the distribution of high-frequency components and low-frequency components is related to the direction of the frequency distribution in the original data. The principle of image compression using wavelet transform is the same as that of the sub-band coding method, which is to decompose the original image signal into different frequency regions. The continuous compression coding method is based on human vision, image statistics, details and structure, and other characteristics. Different compression encoding methods are adopted in the frequency area, thereby reducing the amount of data.

uses wavelet transform for image compression, generally using discrete wavelet transform coding method. Discrete orthogonal wavelets used in image compression are generally constructed from filter functions. For a given digital signal matrix, decompose it into a high-pass and a low-pass sub-signal, and the two are mutually orthogonal. When necessary, each sub-signal can be divided recursively until the required bandwidth is reached, and then analyzed and calculated.

In the field of image coding, wavelet transform coding technology is an emerging image coding method. On the one hand, wavelet coding has the advantages of traditional coding; on the other hand, the multi-resolution transformation characteristics of wavelet transform provide a good mechanism for utilizing the visual characteristics of the human eye. Therefore, wavelet image coding is very promising in the field of image coding with higher compression ratio.

At present, the image compression coding of wavelet transform includes extended zero-tree coding, coding combining zero tree and run length, polynomial approximate fractal coding, multi-wavelet transform image coding, etc.

7. New technology of low bit rate image coding

Another research focus of image coding is extremely low bit rate image compression. Its transmission bit rate is lower than 64kbps, and its application scope will be wider, such as TV telephone and multimedia on PSTN network. E-mail, mobile visual communication, electronic newspapers, interactive multimedia databases, visual games, telemedicine, and assistive communication for the deaf and mute, etc. Some new coding methods that have appeared recently are mostly aimed at encoding extremely low bit rate images. For example, in the multimedia video phone , it requires that the image can be compressed and transmitted over the existing public telephone network, and the compression ratio can reach Thousands of times, it is extremely difficult. For ordinary TV images, it is difficult to achieve such a high compression ratio while ensuring a certain viewing quality. For a typical video phone image, the image content is relatively simple and the movement range is not large. These are conditions that can be exploited in extremely low bit rate image coding.

The current research on extremely low bit rate image coding can be roughly divided into two directions.

(1) Wave-From-Based Coding: The starting point of waveform-based coding is the waveform of the brightness and color difference signals of each pixel in the image, and its various internal statistical characteristics are used for compression coding.

(2) Knowledge-Based Coding: Knowledge-based (sometimes also called model-based) coding is a method of coding from a new perspective. It treats images as three-dimensional objects on a two-dimensional plane. projection. The first step in encoding is to establish a model of the object, and then obtain various parameters of the model (geometry, color, motion, etc.) by analyzing the input image and model, and then encode and transmit the parameters. The decoding end uses the image Comprehensive method to restore images. Therefore, this method is also called analytical and comprehensive coding. This encoding method makes more use of the prior knowledge of the image than the former. It uses parameters (rather than pixel levels) for encoding and transmission, so it can achieve a higher compression ratio.

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