Explain Different Types of Wavelet Based Coding

Wavelet-based coding is a popular technique used for compression of digital signals such as images, audio, and video. It is a lossy compression technique, meaning that it compresses the data by discarding some information in the original signal. In this technique, wavelets are used as basis functions to decompose the signal into multiple levels of detail, where each level contains a different level of information about the signal. The resulting coefficients are then quantized and encoded to reduce the amount of data that needs to be transmitted or stored.

There are several types of wavelet-based coding techniques that are used in practice. In this article, we will discuss the most common types of wavelet-based coding techniques and how they work.

1. Discrete Wavelet Transform (DWT) Based Coding

The Discrete Wavelet Transform (DWT) is the most common wavelet-based coding technique used for compression of images, audio, and video. It decomposes the signal into different frequency sub-bands using a filter bank approach. The DWT can be implemented using several wavelet families such as Haar, Daubechies, Symlet, Coiflet, and Biorthogonal. The choice of wavelet family depends on the characteristics of the signal being compressed and the compression ratio required.

In DWT-based coding, the signal is decomposed into different frequency sub-bands using a multi-resolution analysis. The signal is first passed through a low-pass filter and a high-pass filter to obtain the approximation and detail coefficients, respectively. The approximation coefficients represent the low-frequency content of the signal, while the detail coefficients represent the high-frequency content. The decomposition process is repeated on the approximation coefficients to obtain multiple levels of detail.

The resulting coefficients are then quantized and encoded using entropy coding techniques such as Huffman coding, Arithmetic coding, or Run-length encoding. The quantization process is essential in reducing the amount of data that needs to be transmitted or stored. However, it also introduces some loss of information, which affects the quality of the reconstructed signal.

2. Wavelet Packet Transform (WPT) Based Coding

The Wavelet Packet Transform (WPT) is an extension of the DWT that provides a more flexible decomposition of the signal into different frequency sub-bands. Unlike the DWT, which only decomposes the signal into approximation and detail coefficients, the WPT decomposes the signal into different sub-bands at each level. The resulting sub-bands are called wavelet packets.

In WPT-based coding, the signal is decomposed into different wavelet packets at each level, where each wavelet packet represents a different frequency sub-band. The coefficients are then quantized and encoded using entropy coding techniques such as Huffman coding or Arithmetic coding. The WPT can provide a higher compression ratio than the DWT, but it also requires more computational resources.

3. Embedded Zero-tree Wavelet (EZW) Based Coding

The Embedded Zero-tree Wavelet (EZW) algorithm is a popular wavelet-based coding technique used for compression of images. It is based on the concept of using a tree structure to represent the wavelet coefficients, where the coefficients are organized in a hierarchical manner.

In EZW-based coding, the wavelet coefficients are first transformed using the DWT. The resulting coefficients are then arranged in a hierarchical manner, where the lowest level contains the approximation coefficients, and the higher levels contain the detail coefficients. The tree structure is then used to represent the coefficients in a compressed form.

The EZW algorithm uses a technique called thresholding to remove the insignificant coefficients from the tree structure. The remaining coefficients are then encoded using entropy coding techniques such as Huffman coding or Arithmetic coding. The EZW algorithm provides a high compression ratio with good reconstruction quality, but it also requires more computational resources than other wavelet-based coding. 

Sure, here are a few more types of wavelet-based coding techniques:

4. Set Partitioning in Hierarchical Trees (SPIHT) Based Coding

The Set Partitioning in Hierarchical Trees (SPIHT) algorithm is a wavelet-based coding technique that uses a combination of set partitioning and thresholding to compress the wavelet coefficients. It is similar to the EZW algorithm in that it also uses a tree structure to represent the wavelet coefficients. However, the SPIHT algorithm uses a more efficient set partitioning technique to reduce the number of bits required to represent the coefficients.

In SPIHT-based coding, the wavelet coefficients are first transformed using the DWT. The resulting coefficients are then organized into a tree structure using a sorting algorithm. The tree structure is then used to partition the coefficients into subsets based on their significance. The significant coefficients are then encoded using entropy coding techniques such as Huffman coding or Arithmetic coding.

The SPIHT algorithm provides a high compression ratio with good reconstruction quality, but it also requires more computational resources than other wavelet-based coding techniques.

5. Integer Wavelet Transform (IWT) Based Coding

The Integer Wavelet Transform (IWT) is a wavelet-based coding technique that uses integer arithmetic instead of floating-point arithmetic to perform the wavelet transform. It is similar to the DWT in that it also decomposes the signal into different frequency sub-bands using a filter bank approach. However, the IWT uses integer filters to perform the transform, which reduces the computational complexity and memory requirements.

In IWT-based coding, the signal is first transformed using integer filters to obtain the approximation and detail coefficients. The decomposition process is repeated on the approximation coefficients to obtain multiple levels of detail. The resulting coefficients are then quantized and encoded using entropy coding techniques such as Huffman coding or Arithmetic coding.

The IWT algorithm provides a high compression ratio with good reconstruction quality and requires less computational resources than other wavelet-based coding techniques.

6. Directional Wavelet Transform (DWT) Based Coding

The Directional Wavelet Transform (DWT) is a wavelet-based coding technique that uses directional filters to decompose the signal into different frequency sub-bands. It is similar to the DWT in that it also decomposes the signal into approximation and detail coefficients using a filter bank approach. However, the DWT uses directional filters to extract directional information from the signal.

In DWT-based coding, the signal is first decomposed using directional filters to obtain the approximation and detail coefficients. The decomposition process is repeated on the approximation coefficients to obtain multiple levels of detail. The resulting coefficients are then quantized and encoded using entropy coding techniques such as Huffman coding or Arithmetic coding.

The DWT algorithm provides a high compression ratio with good reconstruction quality and can preserve directional information in the signal. However, it also requires more computational resources than other wavelet-based coding techniques.

7. Wavelet Packet Transform (WPT) Based Coding

The Wavelet Packet Transform (WPT) is a wavelet-based coding technique that uses a binary tree structure to represent the wavelet coefficients. It is similar to the DWT and IWT in that it also decomposes the signal into different frequency sub-bands using a filter bank approach. However, the WPT uses a more flexible tree structure that allows for different levels of detail in different frequency sub-bands.

In WPT-based coding, the signal is first transformed using a filter bank to obtain the approximation and detail coefficients. The decomposition process is then repeated on the detail coefficients to obtain multiple levels of detail. The resulting coefficients are then organized into a binary tree structure based on their frequency and scale. The tree structure is then used to select and encode the most significant coefficients using entropy coding techniques such as Huffman coding or Arithmetic coding.

The WPT algorithm provides a higher compression ratio and better frequency localization than other wavelet-based coding techniques. However, it also requires more computational resources and memory than other techniques.

8. Wavelet Transform Modulus Maxima (WTMM) Based Coding

The Wavelet Transform Modulus Maxima (WTMM) is a wavelet-based coding technique that uses a local maxima detection algorithm to extract the significant wavelet coefficients. It is similar to the EZW and SPIHT algorithms in that it also uses thresholding to reduce the number of bits required to represent the coefficients. However, the WTMM algorithm uses a more flexible approach to extract the significant coefficients.

In WTMM-based coding, the wavelet coefficients are first transformed using the DWT. The resulting coefficients are then analyzed using a local maxima detection algorithm to extract the significant coefficients. The significant coefficients are then quantized and encoded using entropy coding techniques such as Huffman coding or Arithmetic coding.

The WTMM algorithm provides a high compression ratio with good reconstruction quality and is particularly effective in compressing signals with irregular or non-stationary characteristics. However, it also requires more computational resources and memory than other wavelet-based coding techniques.

Overall, these types of wavelet-based coding techniques provide a range of options for efficiently compressing signals while maintaining good reconstruction quality. The choice of which technique to use depends on the characteristics of the signal being compressed and the requirements of the application.