Rate control optimization in embedded wavelet coding
Introduction
The recent growth of data intensive multimedia-based (graphics, audio and video) applications has not only sustained the need for more efficient ways to encode signals and images but has made compression of such signals central to storage and communication technology. There is also an increasing interest in image compression for providing the desired quality distortion or bit rate for each particular application and this requires adequate supervision of the compression process: A coding process should encode the most important information first, and this is an unsolved problem.
In recent years subband image coding, especially wavelet-subband image coding, emerged as an efficient method for image compression (Vetterli and Kovacevic, 1995). The wavelet-based progressive coding approach first introduced by Shapiro, EZW (Shapiro, 1993) relies on the idea that more important information (defined as what decreases a certain quadratic distortion measure the most) should be transmitted first, so the method boils down to ranking the coefficients by bit planes and transmitting the most significant bits first. One of the most successful and practical embedded coders (refinement of the Shapiro coder) is the SPIHT (Said and Pearlman, 1996) image compression method. Their image coding technique first takes a wavelet transform of the input image and then codes the pixels in the wavelet domain in a clever manner using the tree-structured dependencies that result between the pixels in different subbands. In this way, a progressive mode of transmission is achieved, namely that as more bits are transmitted, better quality reconstructed images can be produced at the receiver. The receiver need not wait for all of the information to arrive before decoding the picture, and the decoder can use each additional received bit to improve the previously decoded output. These wavelet-based encoders have been shown to perform better than almost any other existing compression technique. In addition, they have the nice feature of being computationally simple. However, there are two aspects not optimized in the existing coders, that is, the selection of bits to be transmitted at each step of the progressive transmission and the distortion criterion to measure the quality of the successive decoded output. In this paper, we will introduce a new methodology to rate control in progressive image transmission under a theoretic frame provided by the utility theory (Herden et al., 1999) using additionally an alternative to quadratic distortion criteria to quantify the image distortion in each decoded image.
The paper is organized as follows: Section 2 shows the basic elements in the selection problem that is present in an embedded wavelet coding scheme for progressive transmission. Section 3 shows the proposed basic axiomatic for avoiding forms of behavioral inconsistency in the progressive transmission process. Section 4 presents the proposed rate control methodologies which will be used in embedded wavelet image coding and whose experimental use is shown in Section 5.
Section snippets
The objective
A progressive transmission scheme prioritizes the code bits according to their reduction in distortion (e.g., Said and Pearlman, 1996). If the original image is I, the coding is actually done to , where represents a unitary hierarchical subband transformation (Adelson et al., 1987). The 2D array C={ci,j} has the same dimensions of I, and each element ci,j is called transform coefficient at coordinate (i,j) which for the purpose of coding it can be treated as an integer. In a progressive
Basic axiomatic for avoiding forms of behavioral inconsistency
The operational notion of preference between SOTs, formalized by the binary relation ⪯, provides a qualitative basis for comparing SOTs. The following coherence axioms (Axioms 1–3) are to be proposed to provide a minimal set of rules to ensure that qualitative comparisons based on ⪯ cannot have intuitively undesirable implications (following Bernardo and Smith, 1994). Postulate 1 not all the consequences in are equivalent; and The transmission system is able to compare any pair of options concerning the
Rate control for just distribution
Proposition 2 provides, on the basis of the expected utility (Fishburn, 1982), an optimal solution to the problem of choosing, at time t, a SOT Ri for the transmission of a number of bit streams: In accordance with Postulate 1, Postulate 2, Postulate 3, Postulate 4, Postulate 5, Postulate 6, Postulate 7, the rational choice for transmission at truncation time t is to select bit streams associated with the maximum achievable expected increase in utility per coding bit, for
Experimental use of the rate control procedure
In this section we analyze the comparative performance of two progressive compression schemes: REWIC2 that uses the proposed rate control procedure and SPIHT (using its own rate control scheme). For this comparison, we need a proper coder selection procedure. A traditional approach for evaluating the comparative performance of lossy compression methods in an application is to simulate the application in a carefully designed experiment, gather necessary data in a way that interferes with the
Conclusions
In an embedded wavelet scheme for progressive transmission, a tree structure naturally defines the spatial relationship on the hierarchical pyramid. Transform coefficients over each tree correspond to a unique local spatial region of the original image, and they may be coded bit-plane by bit-plane through successive-approximation quantization. After receiving the approximate value of some coefficients, the decoder can obtain a reconstructed image. Here we have shown a rational system for rate
Acknowledgements
This research was sponsored by the Dirección General de Enseñanza Superior, Spanish Board for Science and Technology, (CICYT) under grant TIC2000-1421. Thanks are due to the reviewers for their constructive suggestions.
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Analysis of coding risks in progressive transmission
2012, Signal Processing: Image CommunicationCitation Excerpt :JPEG2000 already performs a sort of analysis in the rate control stage, and comparison with this technique could bring some enlightenment as to which are the most appropriate bits to be appended in the codestream, and in particular, JPIP (JPEG2000 Internet Protocol) [7] could be relevant to better understand modern transmission protocols. Finally, REWIC implements a rate control optimization in embedded wavelet coding in order to perform the progressive transmission, [9]. For SPIHT and SPECK we have used five wavelet levels; while the number of wavelet levels was set to six for REWIC.