Directional Lapped Transforms for Image Coding

In this paper, we present the design of directional lapped transforms for image coding. A lapped transform, which can be implemented by a prefilter followed by a discrete cosine transform (DCT), can be factorized into elementary operators. The corresponding directional lapped transform is generated by applying each elementary operator along a given direction. The proposed directional lapped transforms are not only nonredundant and perfectly reconstructed, but they can also provide a basis along an arbitrary direction. These properties, along with the advantages of lapped transforms, make the proposed transforms appealing for image coding. A block-based directional transform scheme is also presented and integrated into HD Phtoto, one of the state-of-the-art image coding systems, to verify the effectiveness of the proposed transforms.     

A low-complexity image compression approach with single spatial prediction mode and transform

The well-known low-complexity JPEG and the newer JPEG-XR systems are based on block-based transform and simple transform-domain coefficient prediction algorithms. Higher complexity image compression algorithms, obtainable from intra-frame coding tools of video coders H.264 or HEVC, are based on multiple block-based spatial-domain prediction modes and transforms. This paper explores an alternative low-complexity image compression approach based on a single spatial-domain prediction mode and transform, which are designed based on a global image model. In our experiments, the proposed single-mode approach uses an average 20.5 % lower bit-rate than a standard low-complexity single-mode image coder that uses only conventional DC spatial prediction and 2-D DCT. It also does not suffer from blocking effects at low bit-rates.     

Edge-oriented uniform intra prediction

We propose an intra prediction solution to block-based image compression. In order to adapt to local image features during intra prediction, we consider the distinct image singularities within the model of piece-wise smooth functions. With such singularities, i.e., edges in this paper, intra prediction can be performed by solving Laplace equations. Moreover, since edges exhibit spatial correlations, we design a rate-distortion optimized method for edge extraction and edge coding. Our edge-oriented intra prediction thus consists of the prediction of smooth regions as well as the prediction of edges. We compare our intra prediction with that in H.264 and achieve superior performance. Our intra prediction can also be integrated into a block-based image coding scheme, which is comparable to JPEG2000 in terms of objective quality. An important advantage of our intra prediction is the improvement in visual quality at low bit-rate due to the preservation of edges.     

Efficient sign coding and estimation of zero-quantized coefficients in embedded wavelet image codecs

Wavelet transform coefficients are defined by both a magnitude and a sign. While efficient algorithms exist for coding the transform coefficient magnitudes, current wavelet image coding algorithms are not as efficient at coding the sign of the transform coefficients. It is generally assumed that there is no compression gain to be obtained from entropy coding of the sign. Only recently have some authors begun to investigate this component of wavelet image coding. In this paper, sign coding is examined in detail in the context of an embedded wavelet image coder. In addition to using intraband wavelet coefficients in a sign coding context model, a projection technique is described that allows nonintraband wavelet coefficients to be incorporated into the context model. At the decoder, accumulated sign prediction statistics are also used to derive improved reconstruction estimates for zero-quantized coefficients. These techniques are shown to yield PSNR improvements averaging 0.3 dB, and are applicable to any genre of embedded wavelet image codec.     

Lossless image compression with projection-based and adaptive reversible integer wavelet transforms

Reversible integer wavelet transforms are increasingly popular in lossless image compression, as evidenced by their use in the recently developed JPEG2000 image coding standard. In this paper, a projection-based technique is presented for decreasing the first-order entropy of transform coefficients and improving the lossless compression performance of reversible integer wavelet transforms. The projection technique is developed and used to predict a wavelet transform coefficient as a linear combination of other wavelet transform coefficients. It yields optimal fixed prediction steps for lifting-based wavelet transforms and unifies many wavelet-based lossless image compression results found in the literature. Additionally, the projection technique is used in an adaptive prediction scheme that varies the final prediction step of the lifting-based transform based on a modeling context. Compared to current fixed and adaptive lifting-based transforms, the projection technique produces improved reversible integer wavelet transforms with superior lossless compression performance. It also provides a generalized framework that explains and unifies many previous results in wavelet-based lossless image compression.     

Compression of Laplacian pyramids through orthogonal transforms and improved prediction

Scalable representation of visual signals, such as image and video signals, has become a subject of active research since early 1980s. Scalability allows the adaptation of the bit rate and/or the resolution of the transmitted data to the network bandwidth and/or the rendering capability of the receiving device. For many years, spatial scalability has been achieved through wavelets, but recently the Laplacian pyramid (LP) has become an alternative choice because of reduced aliasing in the lower resolutions. In this paper, we focus on the coding efficiency of the LP with a view to transmitting it over a communication channel. In particular, we aim to improve the compression efficiency of the LP detail layers through improved interlayer prediction and orthogonal spatial transforms. First, we consider an LP in the open-loop configuration and propose to improve its rate-distortion performance by compressing it to a critically sampled representation. We derive four different orthogonal spatial transforms from the upsampling and downsampling filters that can achieve this representation, and apply them on the detail layers. The application of these transforms to the detail layers renders a fixed number of transform coefficients either zero or redundant, thus making their transmission unnecessary. Then we consider the compression of an LP in the closed-loop configuration through similar spatial transforms. Because of the introduction of quantization in the prediction loop, these spatial transforms applied on the detail layers do not produce the same number of zero or redundant transform coefficients as in the open-loop case. Nevertheless, the insight obtained from the open-loop coding leads us to enhance the interlayer prediction, and the subsequent application of the spatial transforms to the new detail layers aims to achieve better energy compaction.     

Linear, Worst-Case Estimators for Denoising Quantization Noise in Transform Coded Images

Transform-coded images exhibit distortions that fall outside of the assumptions of traditional denoising techniques. In this paper, we use tools from robust signal processing to construct linear, worst-case estimators for the denoising of transform compressed images. We show that while standard denoising is fundamentally determined by statistical models for images alone, the distortions induced by transform coding are heavily dependent on the structure of the transform used. Our method, thus, uses simple models for the image and for the quantization error, with the latter capturing the transform dependency. Based on these models, we derive optimal, linear estimators of the original image that are optimal in the mean-squared error sense for the worst-case cross correlation between the original and the quantization error. Our construction is transform agnostic and is applicable to transforms from block discrete cosine transforms to wavelets. Furthermore, our approach is applicable to different types of image statistics and can also serve as an optimization tool for the design of transforms/quantizers. Through the interaction of the source and quantizer models, our work provides useful insights and is instrumental in identifying and removing quantization artifacts from general signals coded with general transforms. As we decouple the modeling and processing steps, we allow for the construction of many different types of estimators depending on the desired sophistication and available computational complexity. In the low end of this spectrum, our lookup table based estimator, which can be deployed in low complexity environments, provides competitive PSNR values with some of the best results in the literature.     

Adaptive predictor based on maximally flat halfband filter inlifting scheme

For complex short time-varying signals, a high-order predictor does not always yield good performance. For this, we investigate the use of a short-order adaptive predictor. Since the maximally flat filters are the optimal predictors for polynomial signal prediction, the adaptation is based on the combination of a set of maximally flat filters. For compression efficiency, the dynamic ranges of the weighting variables are specially considered. For this, based on the Bernstein filters, another form to represent the weighting variables is used. These two sets of weighting coefficients can be transformed into each other with a simple linear transform. Thus, the adaptation can be made in both the time domain and the frequency domain. For block-based image coding, the least square criterion is used to derive the weighting coefficients. Experimental results show that the adaptive predictor performs better than the S+P transform, the median edge detector (MED), and the gradient adjusted predictor (GAP)     

Integer lapped transforms and their applications to image coding

This paper proposes new integer approximations of the lapped transforms, called the integer lapped transforms (ILT), and studies their applications to image coding. The ILT are derived from a set of orthogonal sinusoidal transforms having short integer coefficients, which can be implemented with simple integer arithmetic. By employing the same scaling constants in these integer sinusoidal transforms, integer versions of the lapped orthogonal transform (LOT), the lapped biorthogonal transform (LBT), and the hierarchical lapped biorthogonal transform (HLBT) are developed. The ILTs with 5-b integer coefficients are found to have similar coding gain (within 0.06 dB) and image coding performances as their real-valued counterparts. Furthermore, by representing these integer coefficients as sum of powers-of-two coefficients (SOPOT), multiplier-less lapped transforms with very low implementation complexity are obtained. In particular, the implementation of the eight-channel multiplier-less integer LOT (ILOT), LBT (ILBT), and HLBT (IHLBT) require 90 additions and 44 shifts, 98 additions and 59 shifts, and 70 additions and 38 shifts, respectively.     

On the performance of linear phase wavelet transforms in lowbit-rate image coding

The behavior of linear phase wavelet transforms in low bit-rate image coding is investigated. The influence of certain characteristics of these transforms such as regularity, number of vanishing moments, filter length, coding gain, frequency selectivity, and the shape of the wavelets on the coding performance is analyzed. The wavelet transforms performance is assessed based on a first-order Markov source and on the image quality, using subjective tests. More than 20 wavelet transforms of a test image were coded with a product code lattice quantizer with the image quality rated by different viewers. The results show that, as long as the wavelet transforms perform reasonably well, features like regularity and number of vanishing moments do not have any important impact on final image quality. The influence of the coding gain by itself is also small. On the other hand, the shape of the synthesis wavelet, which determines the visibility of coding errors on reconstructed images, is very important. Analysis of the data obtained strongly suggests that the design of good wavelet transforms for low bit-rate image coding should take into account chiefly the shape of the synthesis wavelet and, to a lesser extent, the coding.     

Block-based SVD image watermarking in spatial and transform domains

The idea of this paper is to implement an efficient block-by-block singular value (SV) decomposition digital image watermarking algorithm, which is implemented in both the spatial and transforms domains. The discrete wavelet transform (DWT), the discrete cosine transform and the discrete Fourier transform are exploited for this purpose. The original image or one of its transforms is segmented into non-overlapping blocks, and consequently the image to be inserted as a watermark is embedded in the SVs of these blocks. Embedding the watermark on a block-by-block manner ensures security and robustness to attacks such like Gaussian noise, cropping and compression. The proposed algorithm can also be used for colour image watermarking. A comparison study between the proposed block-based watermarking algorithm and the method of Liu is performed for watermarking in all domains. Simulation results ensure that the proposed algorithm is more effective than the traditional method of Liu, especially when the watermarking is performed in the DWT domain.     

Wavelet packet image coding using space-frequency quantization

We extend our previous work on space-frequency quantization (SFQ) for image coding from wavelet transforms to the more general wavelet packet transforms. The resulting wavelet packet coder offers a universal transform coding framework within the constraints of filterbank structures by allowing joint transform and quantizer design without assuming a priori statistics of the input image. In other words, the new coder adaptively chooses the representation to suit the image and the quantization to suit the representation. Experimental results show that, for some image classes, our new coder gives excellent coding performance.     

Multiview video compression with 1-D transforms

Many alternative transforms have been developed recently for improved compression of images, intra prediction residuals or motion-compensated prediction residuals. In this paper, we propose alternative transforms for multiview video coding. We analyze the spatial characteristics of disparity-compensated prediction residuals, and the analysis results show that many regions have 1-D signal characteristics, similar to previous findings for motion-compensated prediction residuals. Signals with such characteristics can be transformed more efficiently with transforms adapted to these characteristics and we propose to use 1-D transforms in the compression of disparity-compensated prediction residuals in multiview video coding. To show the compression gains achievable from using these transforms, we modify the reference software (JMVC) of the multiview video coding amendment to H.264/AVC so that each residual block can be transformed either with a 1-D transform or with the conventional 2-D Discrete Cosine Transform. Experimental results show that coding gains ranging from about 1–15% of Bjontegaard-Delta bitrate savings can be achieved.     

Regularity-constrained pre- and post-filtering for block DCT-based systems

It is well known that the traditional block transform can only have at most one degree of regularity. In other words, by retaining only one subband, these transforms, including the popular discrete cosine transform (DCT), can only capture the constant signal. The ability to capture polynomials of higher orders is critical in smooth signal approximation, minimizing blocking effects. This paper presents the theory, design, and fast implementation of regularity constrained pre-/post-filters for block-based decomposition systems. We demonstrate that simple pre-/post-filtering modules added to the current block-based infrastructure can help the block transform capture not only the constant signal but the ramp signal as well. Moreover, our proposed framework can be used to generate various fast symmetric M-band wavelets with up to two degrees of regularity.     

Efficient Block-Based Frequency Domain Wavelet Transform Implementations

Subband decompositions for image coding have been explored extensively over the last few decades. The condensed wavelet packet (CWP) transform is one such decomposition that was recently shown to have coding performance advantages over conventional decompositions. A special feature of the CWP is that its design and implementation are performed in the cyclic frequency domain. While performance gains have been reported, efficient implementations of the CWP (or more generally, efficient implementations of cyclic filter banks) have not yet been fully explored. In this paper, we present efficient block-based implementations of cyclic filter banks along with an analysis of the arithmetic complexity. Block-based cyclic filter bank implementations of the CWP coder are compared with conventional subband/wavelet image coders whose filter banks are implemented in the time domain. It is shown that block-based cyclic filter bank implementations can result in CWP coding systems that outperform the popular image coding systems both in terms of arithmetic complexity and coding performance.      

BOT's based on nonuniform filter banks

Parallels between orthogonal transforms and filter banks have been drawn before. Block orthogonal transform (BOT) is a special case of orthogonal transform where a nonoverlapping window is used. We relate BOTs to filter banks. Specifically, we show that any BOT can be shown as a perfect reconstruction filter bank, and any tree-structured perfect reconstruction filter bank or any orthonormal filter bank for which no filter length exceeds its decimation factor can be shown as a BOT. We then show that all conventional BOTs map to uniform filter banks. A construction method to design a BOT from any nonuniform filter bank is presented, and finding an optimal tree structure (in the sense of transform coding gain) for a given source is also discussed. The results show that the optimal, nonuniform BOT outperforms uniform BOTs having either the same number of bands or the same size in most cases     

Fractional cosine, sine, and Hartley transforms

In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. We introduce several new transforms. They are all the generalization of the cosine, sine, or Hartley transform. We first derive the fractional cosine, sine, and Hartley transforms (FRCT/FRST/FRHT). They are analogous to the FRFT. Then, we derive the canonical cosine and sine transforms (CCT/CST). They are analogous to the LCT. We also derive the simplified fractional cosine, sine, and Hartley transforms (SFRCT/SFRST/SFRHT). They are analogous to the SFRFT and have the advantage of real-input-real-output. We also discuss the properties, digital implementation, and applications (e.g., the applications for filter design and space-variant pattern recognition) of these transforms. The transforms introduced in this paper are very efficient for digital implementation. We can just use one half or one fourth of the real multiplications required for the FRFT and LCT to implement them. When we want to process even, odd, or pure real/imaginary functions, we can use these transforms instead of the FRFT and LCT. Besides, we also show that the FRCT/FRST, CCT/CST, and SFRCT/SFRST are also useful for the one-sided (t ∈ [0, ∞]) signal processing     

The integer transforms analogous to discrete trigonometric transforms

The integer transform (such as the Walsh transform) is the discrete transform that all the entries of the transform matrix are integer. It is much easier to implement because the real number multiplication operations can be avoided, but the performance is usually worse. On the other hand, the noninteger transform, such as the DFT and DCT, has a good performance, but real number multiplication is required. W derive the integer transforms analogous to some popular noninteger transforms. These integer transforms retain most of the performance quality of the original transform, but the implementation is much simpler. Especially, for the two-dimensional (2-D) block transform in image/video, the saving can be huge using integer operations. In 1989, Cham had derived the integer cosine transform. Here, we will derive the integer sine, Hartley, and Fourier transforms. We also introduce the general method to derive the integer transform from some noninteger transform. Besides, the integer transform derived by Cham still requires real number multiplication for the inverse transform. We modify the integer transform introduced by Cham and introduce the complete integer transform. It requires no real number multiplication operation, no matter what the forward or inverse transform. The integer transform we derive would be more efficient than the original transform. For example, for the 8-point DFT and IDFT, there are in total four real numbers and eight fixed-point multiplication operations required, but for the forward and inverse 8-point complete integer Fourier transforms, there are totally 20 fixed-point multiplication operations required. However, for the integer transform, the implementation is simpler, and many of the properties of the original transform are kept.     

Integer sinusoidal transforms for image processing

The sine and cosine transforms, which are popular transforms for image coding, are members of a sinusoidal transform family. Each member of the family is the optimal KLT of a Markov process. This paper derives the conditions under which the order-8 sinusoidal transforms can be approximated by orthogonal integer transforms which can be implemented using integer arithmetic. Some integer transforms are derived as examples. The results show that for the popular even sine-1, even sine-2 and the cosine transforms, there is an infinite number of integer transforms and some have their transform component magnitudes less than eight. In LSI implementation, if low implementation cost and fast computation speed are paramount, then an integer transform of small component magnitudes can be chosen. If better performance is desired, integer transforms whose elements have larger magnitudes can be used. The availability of many integer transforms provides a design engineer the freedom to trade-off performance against simple implementation and speed.     

Performance analysis of space-time MMSE multiuser detection for coded DS-CDMA systems in multipath fading channels

This paper investigates the use of convolutional coding in space-time minimum mean-square-error (MMSE) multiuser-based receivers over asynchronous multipath Rayleigh fading channels. We focus on the performance gain attained through error control coding when used with binary-phase-shift-keyed modulation (BPSK) and multiuser access based on direct sequence-code-division multiple access (DS-CDMA). In our analysis, we derive an approximation for the uncoded probability of bit-error in multipath fading channels. This bit-error rate (BER) approximation is shown to be very accurate when compared to the exact performance. For a convolutionally coded system, we obtain a closed form expression for the bit-error rate upper bound. This error bound is noted to be tight as the number of quantization levels increased beyond eight. Using our theoretical results, we obtain an estimate for the achieved user-capacity that accrues due to error control coding. It is found that using convolutional coding with 3-bit soft-decision decoding, a user-capacity gain as much as 300% can easily be achieved when complete fading state information plus ideal channel interleaving are assumed.