# Adaptive Vector Quantization for Lossy Compression of Image Sequences +
## 1 Introduction  
Data compression techniques, based on the _Vector Quantization_ (VQ), are widely used in several scenarios. For instance, VQ-based techniques are used for the compression of multispectral [1] and hyperspectral images [2], static images [3], etc.  
The VQ is a process that allows the approximation of sampled analog data (e.g., speech, images, etc.). Indeed, by means of the VQ, the input data is subdivided into blocks, denoted as _vectors_, and each vector is replaced by a _similar_ one (or equal, when possible) stored into a static dictionary of codebook vectors (denoted as _codewords_) [4]. In the first stage, a VQ-based encoder calculates all the distances (according to a given distortion measure) between the input block (\(X_{k}\)) and each one of the blocks into the codewords. Subsequently, the index \(i\) of the block, which is more similar with respect to the input block, is identified, as shown in Figure 0(a). Thus, the index \(i\) can be transmitted to the decoder or stored into a file. On the other hand, a VQ-based decoder receives (or reads) the index \(i\) and can reconstruct the appropriate approximated block, as shown in Figure 0(b). It is important to point out that the codewords must be identical for the encoder as well as for the decoder. Moreover, the size of an index is related to the size of the codewords (denoted as \(N\)), since an index is composed by \(\log_{2}N\) bits.  
The capabilities of the VQ approach are combined with the characteristics of the _dictionary-based techniques_ by [PERSON] and [PERSON], in order to provide an efficient scheme for the lossy compression of grayscale image [5]. The method they proposed is referred to as the _Adaptive Vector Quantization_ (AVQ) algorithm.  
A well-known dictionary-based approach is the one outlined by [PERSON] and [PERSON] (often referred to as LZ2) in [6]. The LZ2-based (or LZ78-based) approaches are mainly used for the textual data compression. Basically, such approaches encode the repeated occurrences of substrings through an index of a dynamically created _dictionary_. Since the dictionary is dynamically created, an LZ2 scheme can perform the encoding in a single pass and does not need a priori statistical knowledge of the input data.  
Analogously to the LZ2 approaches, the encoder of the AVQ algorithm is capable of dynamically creating a dictionary and is able to encode the input data in a single pass.  
In this paper, we focus on the key aspects of the AVQ algorithm, by reviewing its logical functioning and its architectural elements. Subsequently, we focus on some easy-to-implement design concepts to extend the AVQ algorithm, in order to allow the lossy compression of image sequences. The proposed scheme we denoted as _Adaptive Vector Quantization for Image Sequences_ (AVQIs), which exploits the _temporal correlation_ (i.e., the correlation among adjacent frames of a sequence) and is generally high among the frames of an image sequence.  
The paper is organized as follows: Section 2 briefly reviews the AVQ algorithm and its fundamental aspects. In Section 3, we explain the logical concepts related to the AVQIs algorithm. In Section 4, we report and discuss the preliminary test results that we achieved by our scheme. Finally, we draw our conclusions and outline future research directions.