This letter proposes a fast dual-layer lossless coding for high dynamic range images (HDRIs) in the Radiance format. The coding, which consists of a base layer and a lossless enhancement layer, provides a standard dynamic range image (SDRI) without requiring an additional algorithm at the decoder and can losslessly decode the HDRI by adding the residual signals (residuals) between the HDRI and SDRI to the SDRI, if desired. To suppress the dynamic range of the residuals in the enhancement layer, the coding directly uses the mantissa and exponent information from the Radiance format. To further reduce the residual energy, each mantissa is modeled (estimated) as a linear function, i.e., a simple linear regression, of the encoded-decoded SDRI in each region with the same exponent. This is called simple linear regressive mantissa estimator. Experimental results show that, compared with existing methods, our coding reduces the average bitrate by approximately 1.57–6.68% and significantly reduces the average encoder implementation time by approximately 87.13–98.96%.

To efficiently compress raw camera images captured using a color filter array (CFA-sampled raw images), wavelet-based spectral-spatial transforms (WSSTs) that change a CFA-sampled raw image from an RGB color space into a decorrelated color space have been presented. This study introduces weighted WSSTs (WWSSTs) that work especially for the CFA-sampled raw images with many edges well. The WWSSTs are obtained by considering that each predict step of the conventional WSSTs is constructed by a combination of two 1-D diagonal transforms and by weighting them along the edge directions in the images. The experiments at JPEG 2000-based lossless and lossy compression basically show that compared with the WSSTs, our WSSTs improve the results for the images with many edges by about 0.04 bpp in LBRs, 2.10 [%] in BD-rates, and 0.12 dB in BD-PSNRs while keeping the compression efficiency for the general images.

This letter proposes a fast implementation of the regularity-constrained discrete sine transform (R-DST). The original DSTleaksthe lowest frequency (DC: direct current) components of signals into high frequency (AC: alternating current) subbands. This property is not desired in many applications, particularly image processing, since most of the frequency components in natural images concentrate in DC subband. The characteristic of filter banks whereby they do not leak DC components into the AC subbands is calledregularity. While an R-DST has been proposed, it has no fast implementation because of the singular value decomposition (SVD) in its internal algorithm. In contrast, the proposed regularity-constrained fast sine transform (R-FST) is obtained by just appending a regularity constraint matrix as a postprocessing of the original DST. When the DST size is$M\times M$($M=2^\ell$,$\ell \in \mathbb {N}_{\geq 1}$), the regularity constraint matrix is constructed from only$M/2-1$rotation matrices with the angles derived from the output of the DST for the constant-valued signal (i.e., the DC signal). Since it does not require SVD, the computation is simpler and faster than the R-DST while keeping all of its beneficial properties. An image processing example shows that the R-FST has fine frequency selectivity with no DC leakage and higher coding gain than the original DST. Also, in the case of$M=8$, the R-FST saved approximately$0.126$seconds in a 2-D transformation of$512\times 512$signals compared with the R-DST because of fewer extra operations.

Codecs using spectral-spatial transforms efficiently compress raw camera images captured with a color filter array (CFA-sampled raw images) by changing their RGB color space into a decorrelated color space. This study describes two types of spectral-spatial transform, called extended Star-Tetrix transforms (XSTTs), and their edge-aware versions, called edge-aware XSTTs (EXSTTs), with no extra bits (side information) and little extra complexity. They are obtained by (i) extending the Star-Tetrix transform (STT), which is one of the latest spectral-spatial transforms, to a new version of our previously proposed wavelet-based spectral-spatial transform and a simpler version; (ii) considering that each 2D predict step of the wavelet transform is a combination of two 1D diagonal or horizontal-vertical transforms; (iii) weighting the transforms along the edge directions in the images. Compared with XSTTs, the EXSTTs can decorrelate CFA-sampled raw images well: they reduce the difference in energy between the two green components by about 3.38-30.08 % for high-quality camera images and 8.97-14.47 % for mobile phone images. The experiments on JPEG 2000-based lossless and lossy compression of CFA-sampled raw images show better performance than conventional methods. For high-quality camera images, the XSTTs/EXSTTs produce results equal to or better than the conventional methods: especially for images with many edges, the type-I EXSTT improves them by about 0.03-0.19 bpp in average lossless bitrate and the XSTTs improve them by about 0.16-0.96 dB in average Bjøntegaard delta peak signal-to-noise ratio. For mobile phone images, our previous work perform the best, whereas the XSTTs/EXSTTs show similar trends to the case of high-quality camera images.

A recent attention of JPEG format-compliant encryptions has been concentrated to randomize the specific syntaxes of JPEG file interchange format (JFIF) or to flip the signs of quantized discrete cosine transform (QDCT) coefficients. Although the random sign flip (RSF) achieves low-complexity encryption while preserving the JPEG coding efficiency, the texture information represented by nonzero AC coefficients are still easy to reveal for an attacker using replacement attacks. To reinforce the perceptual degradation and the texture protection at the same complexity as the RSF, we propose an AC prediction error propagation-based encryption (AC-WPE) in the JPEG QDCT domain. Since the AC-WPE encrypts the coefficient signs in the residual QDCT domain obtained by a provisional AC predictor such as differential pulse-code modulation (DPCM) and propagates the encrypted prediction errors among the several blocks by the AC reconstructor, the attack resilience is obviously reinforced. Moreover, to suppress the decrease in coding efficiency, we introduce the randomized prediction intervals into the AC predictor/reconstructor. Experiments with JPEG encryption show that the AC-WPE reinforces the perceptual degradation and the resilience to the replacement attacks, while reasonably expensing the bitrate overheads of crypto-compressed images.

We propose a finely tunable JPEG format-compliant perceptual encryption (FE) with two novel strategies: (i) bitcuboid-based encryption (BE) and (ii) exception-free signed binarization (ESB). BE is an intra- and inter-bitplane encryption technique that provides finely tunable perceptual degradation by encrypting constrained subspaces (‘bitcubes’) of a cuboid-shaped bit set (‘bitcuboid’). ESB is a binarization technique that redecimalizes encrypted binary sequences into signed decimal coefficients without any exception-handling by shifting the negative binary sequences one-by-one. BE with ESB (BEESB) is applied to the quantized discrete cosine transform (QDCT) domain in JPEG compression. The results of our first experiment show that the BE attains fine tunability, which means scalability of the perceptual degradation level with a single encryption method, by encrypting bitcubes of various types and sizes combinatorially. The results of our second experiment show that the BEESB suppresses the bitrate overheads and that BEESB with one of the most secure options suppresses approximately 0.80-187.58% more of the bitrate overheads in terms of Bjøntegaard delta (BD)-rate compared with conventional methods except for some ones. The results of our third experiment show that BEESB has high resilience against attacks.

We propose a perceptual encryption within JPEG compression (EWJ). Although some of the conventional EWJs have the `tun-ability,' which is a property of how many perceptual degradation levels can be provided with the single encryption technique, it is insufficient because either strong level of security or low bitrate overhead is regarded as important. The proposed EWJ detects the specific subspaces of the bits in the quantized discrete cosine transform (QDCT) coefficient blocks (`bitcubes'), such that the non-zero bits crowd, and then the bits are permuted within each bitcube, i.e., not only within each bitplane like the conventional EWJs but also between adjacent bitplanes. The experiments show that the bitcube-based EWJ actually provides more flexible tunability than the conventional EWJs, while compromising the relation between the bitrate overhead and the attack robustness.

A raw image captured by a color filter array (CFA), such as a Bayer pattern, is usually compressed after demosaicing with some processings (denoising, deblurring, tone-mapping, and so on). However, since photographers, designers, and high-end users prefer to work with the raw image sampled by CFA (referred to as “raw image”) directly, a raw image should be compressed before demosaicing. For effective raw image compression, this study introduces variable macropixel spectral-spatial transforms (VMSSTs), that can successfully decorrelate not only Bayer raw images but any other pure-color (RGB) ones. The proposed VMSSTs are designed by the following two steps: 1) intra-color decorrelation and 2) inter-color decorrelation. In lossless compression with JPEG 2000, compared with methods which do not use transforms, the VMSSTs reduced the average bitrates of three types of CFAs: from approximately 0.09 to 0.12 bpp for the modified Bayer CFA, from 0.25 to 0.65 bpp for the diagonal stripe CFA, and from 0.33 to 0.70 bpp for the Fujifilm X-Trans CFA due to their high color decorrelation efficiency. In addition, in lossy compression with JPEG 2000, compared with a rearranged method, the VMSSTs improved the average bitrates of the Bjøntegaard delta by around 3.97%, 14.95%, and 18.65% for each CFA model, respectively. Although a data-dependent adaptive transformation, the Karhunen-Loève transform (KLT), showed the best performance in lossy compression, the introduced VMSSTs have shown performances comparable to those of the KLT in lossless compression, despite their simple structures.

Spectral-spatial transforms (SSTs) change a raw camera image captured using a color filter array (CFA-sampled image) from an RGB color space composed of red, green, and blue components into a decorrelated color space such as YDgCbCr or YDgCoCg color space composed of luma, difference green, and two chroma components. This paper describes three types of wavelet-based SST (WSST) obtained by reorganizing all of the existing SSTs covered in this paper. First, we introduce three types of macropixel SST (MSST) implemented within each 2×2 macropixel. Next, we focus on 2-channel Haar wavelet transforms, which are simple wavelet transforms, and 3-channel Haar-like wavelet transforms in each MSST and replace the Haar and Haar-like wavelet transforms with Cohen-Daubechies-Feauveau (CDF) 5/3 and 9/7 wavelet transforms, which are customized on the basis of the original pixel positions in two-dimensional (2D) space. Although the test data set is not big, in lossless CFA-sampled image compression based on JPEG 2000, the WSSTs improve the bitrates by about 1.67 to 3.17 % compared with not using a transform and the WSSTs that use 5/3 wavelet transforms improve the bitrates by about 0.31 to 0.71 % compared with the best existing SST. Moreover, in lossy CFA-sampled image compression based on JPEG 2000, the WSSTs show about 2.25 to 4.40 dB and 26.04 to 49.35 % in the Bjýntegaard metrics (BD-PSNRs and BD-rates) compared with not using a transform and the WSSTs that use 9/7 wavelet transforms improve the metrics by about 0.13 to 0.40 dB and 2.27 to 4.80 % compared with the best existing SST.

We present a novel image boundary extension and mean value extension (MVE) for directional lapped transforms, particularly cosine-sine modulated lapped transforms (CSMLTs). Lapped transforms are usually used with an extension technique, such as periodic extension (PE) or symmetric extension (SE), for nonexpansive convolution at signal boundaries. When directional textures (oblique lines and curves) appear at the 2D signal (image) boundaries, both PE and SE produce directional discontinuities, which degrade the sparsity of the transformed coefficients, especially in the case of directional lapped transforms. MVE reduces the discontinuities for directional textures better than PE or SE do; it thus improves the efficiency of the sparse representation based on directional lapped transforms. Moreover, to reduce computational costs compared with those of directional lapped transforms, we introduce new directional block transforms called cosine-sine modulated block transforms. These new transforms are derived from a minimum tile processing (tiling) of M-band CSMLTs with 2M filter lengths and nonexpansive convolutions. The resulting directional block transforms, particularly in the case of the MVE, have richer directional selectivity and have better performance compared with a discrete Fourier transform as shown in experiments.

This paper redefines a block-lifting structure of M-channel (M ∈ N, M ≥ 2) filter banks and proposes an efficient reversible nonexpansive convolution at the boundaries for lossy-to-lossless image coding. The previous studies left two problems. One is that the conventional lifting-based filter banks (FBs) are restricted to having equal analysis/synthesis filter lengths. We derive block-lifting-based FBs (BLFBs) with not only equal analysis/synthesis filter lengths but also the longer synthesis filter lengths than those of the analysis banks. The other problem is that the conventional lifting-based FBs without the linear-phase property, such as BLFBs, cannot implement the conventional smooth nonexpansive convolution at the boundaries because of the rounding error in each lifting. We solve the boundary problem by using an efficient reversible nonexpansive convolution derived from a nonexpansive convolution for nonlinear-phase FBs with paraunitariness. We show that the redefined BLFBs with the efficient reversible nonexpansive convolution perform well at lossy-to-lossless image coding.

This paper discusses reversible color transforms, in which a raw camera image captured using a color filter array (CFA) is from red, green, and blue (RGB) color space to YDgCoCg color space for lossless compression. We found that conventional reversible color transforms (YDgCoCg transforms) are composed of three Haar wavelets, which are simple type of wavelet. Since the finding means that the YDgCoCg transforms on the basis of other wavelets that can more accurately predict pixels of interest in the predict steps have the potential to generate more sparse signals, we replaced Haar wavelets in the YDgCoCg transforms with Cohen-Daubechies-Feauveau (CDF) 5/3 and 9/7 wavelets, which were customized on the basis of the original pixel positions in two-dimensional (2D) space. The experimental results show that the extended YDgCoCg (YDgCoCg-X) transforms, which achieve higher sparsity, outperformed the conventional transforms when they are applied to the color transform parts in the JPEG 2000 and JPEG extended range (XR) lossless modes.

Directional block transforms (DBTs), such as discrete Fourier transforms, are basically less efficient for sparse image representation than directional overlapped transforms, such as curvelet and contourlet, but have advantages in practical computation, such as less computational cost, less amount of memory usage to be used, and parallel processing. In order to realize efficient DBTs, this paper proposes directional discrete cosine transforms (DDCTs) by using discrete cosine and sine transforms. The resulting transforms provide richer directional orientations of atoms than conventional DBTs, and thus they are expected to be more efficient for image analysis and processing. In experiments, we evaluate DDCTs with conventional DBTs in image recovery by a convex optimization.

This study presents a pseudo reversible symmetric extension (P-RevSE) that solves the signal boundary problem of lifting-based nonlinear-phase paraunitary filter banks (L-NLPPUFBs), which have high compression rates thanks to their not having a constraint on the linear-phase property unlike the existing transforms used in image coding standards. The conventional L-NLPPUFBs with a periodic extension (PE) yield annoying artifacts at the signal boundaries. However, the P-RevSE is implemented smoothly at the signal boundaries by using a nonexpansive convolution of a symmetric extension (SE) and determinant control for the lifting factorization. Although the determinant control causes a pseudo SE, not a true SE, the resulting L-NLPPUFB with P-RevSE outperforms not only the L-NLPPUFB with PE but also the current transform used in JPEG XR.

This paper presents lifting structures for hierarchical lapped transforms (HLTs) that are highly compatible with the Joint Photographic Experts Group (JPEG) eXtended Range (XR) standard and that are lower in complexity in terms of the number of operations and lifting steps than the existing HLT in JPEG XR. Two structures (TRRand THH), called Householder-lifting structures, are obtained using a lifting factorization followed by a Householder factorization of a nonseparable 2D transform of rotation matrices. The third structure (THR) is simply derived from a combination of a Hadamard transform (THH) and two rotation matrices. The floating-point lifting coefficients are approximated as dyadic values, as in the existing structures of JPEG XR, because doing so costs less, thanks to the structures having only adders and shifters without multipliers. Although the new THHdoes not outperform the existing structure, the new TRRhas one fewer adder, one fewer shifter, and four fewer lifting steps than the existing one. Moreover, the new THRnot only has one fewer adder, three fewer shifters, and two fewer lifting steps, but also can reuse THH, i.e., it can be used to make a more stylish codec. We show that these lower complexity HLTs are comparable in performance to the existing HLT at lossy-to-lossless image coding and at the same time highly compatible with JPEG XR.

This study presents a class of four-channel multiplierless reversible Hadamard transforms (HTs), called lifting-Householder-based HT (LiftH2T), for various signal processing and communication applications. This class is obtained by using a lifting-Householder factorization of a particular 4 × 4 symmetric orthogonal matrix and its application to a four-channel HT. In spite of the simple multiplierless structure with only nine adders, one shifter, and three process steps, it basically outperforms the integer HT (IntHT) and lifting-based HT (LiftHT) in the JPEG XR standard at lossy-to-lossless image coding, thanks to its considering the dynamic range and having less rounding error.

We extend an original lapped transform (LT) and use block-lifting factorization to get an extended block-lifting-based LT (XBL-LT). The block-lifting structure maps integer input signals to integer output signals and results in a reversible transform that reduces rounding errors by merging many rounding operations. Although other such block-lifting-based LTs (BL-LTs) have been proposed, they are forcibly constrained by the use of discrete cosine transform (DCT) matrices. In contrast, XBL-LT is DCT-unconstrained and hence also embodies the DCT-constrained form. Furthermore, it has fewer rounding operations by merging the scaling factor with block-lifting coefficients. The both DCT-constrained and unconstrained XBL-LTs perform well at lossy-to-lossless image coding which has scalability from lossless data to lossy data.

We propose a 2D non-separable block-lifting structure (2D-NSBL) that is easily formulated from the 1D separable block-lifting structure (1D-SBL) and 2D non-separable lifting structure (2D-NSL). The 2D-NSBL can be regarded as an extension of the 2D-NSL, because a two-channel 2D-NSBL is completely equivalent to a 2D-NSL. We apply the 2D-NSBL to M-channel ( M=2(n), n ∈ N) perfect reconstruction filter banks (PRFBs). The 2D-NSBL-based PRFBs outperform 1D-SBL-based PRFBs at lossy-to-lossless coding, whose image quality is scalable from lossless data to high compressed lossy data, because their rounding errors are reduced by merging many rounding operations.

We present a realization of reversible lapped transforms (RevLTs) with simplified implementations, which are constructed by DCT and DST matrices, adders, and bit-shifters, for lossy-to-lossless image coding in this paper. Each DCT or DST matrix is directly used to each lifting coefficient block and it is called DCT-lifting structure. The structure is obtained by considering parallel processing of two `same' type LTs and using DCT-lifting factorizations as our previous work. Furthermore, the Hadamard transform and scaling parts in the RevLTs are effectively implemented by extending 2D non-separable lifting structures derived from lifting-based lapped transform (L-LT) used for JPEG XR, the newest image coding standard. As a result, the proposed RevLTs achieve not only simplified implementations with any block size, but also comparable lossy-to-lossless image coding performance to the conventional RevLTs.

We present an effective image boundary processing for M-channel (M ∈ IN, M ≥ 2) lifting-based linear-phase filter banks that are applied to unified lossy and lossless image compression (coding), i.e., lossy-to-lossless image coding. The reversible symmetric extension we propose is achieved by manipulating building blocks on the image boundary and reawakening the symmetry of each building block that has been lost due to rounding error on each lifting step. In addition, complexity is reduced by extending nonexpansive convolution, called reversible symmetric nonexpansive convolution, because the number of input signals does not even temporarily increase. Our method not only achieves reversible boundary processing, but also is comparable with irreversible symmetric extension in lossy image coding and outperformed periodic extension in lossy-to-lossless image coding.

The multiplierless fast Fourier transform (FFT) with dyadic-valued (rational) coefficients is important for many signal processing tools. The proposed lifting based FFT (L-FFT) based on fast Hartley transform (FHT) has a simpler structure than existing ones because fewer lifting steps need to be approximated. In addition, it has a structure of real-valued calculation followed by complex-valued parts, thereby it requires fewer memories for the internal implementation than the conventional FFTs.

This paper presents a realization of integer fast lapped biorthogonal transform (FLBT) via applications of discrete cosine transform (DCT) matrices and dyadic-valued factors for lifting coefficient blocks. It is obtained by using the block-lifting factorization as our previous work and easy matrix manipulations. The proposed FLBT has higher coding performance and fewer rounding operations than the conventional methods. The practicality of the proposed FLBT is validated through lossy-to-lossless image compression (coding) simulation which unifies lossy and lossless image coding.

Discrete cosine transform (DCT) is known as efficient frequency transform, and when it is implemented on software/hardware, multiplier is undesirable for faster implementation. This paper presents a realization of multiplierless fast DCT for lossy image/video coding on arbitrary devices. First, the proposed DCT is constructed by using fast Hartley transform (FHT). Next, the redundancy of the structure is eliminated by using several characteristics of rotation matrix. Then, multiplierless DCT is obtained by approximating rotation matrices to multiplierless lifting structures with adders and bit-shifters. Finally, the proposed DCT is validated by comparing with the conventional DCTs in image coding.

This paper presents an effective signal boundary solution in lossy-to-lossless image coding which is the unification of lossy and lossless image coding. Although M-channel filter banks (FBs) for lossy image coding have several effective signal boundary solutions, M-channel lifting based FBs (L-FBs) for lossless image coding do not have such an effective signal boundary solutions due to rounding error in each lifting step. This paper proposes reversible non-expansive symmetric convolution for M-channel lifting based linear-phase FBs (L-LPFBs) to apply lossy-to-lossless image coding. Our proposal is validated by comparing with the periodic extension in lossy-to-lossless image coding.

Generalized block-lifting factorization of M-channel (M > 2) biorthogonal filter banks (BOFBs) for lossy-to-lossless image coding is presented in this paper. Since the proposed block-lifting structure is more general than the conventional lifting factorizations and does NOT require many restrictions such as paraunitary, number of channels, and McMillan degree in each building block unlike the conventional lifting factorizations, its coding gain is higher than that of the previous methods. Several proposed BOFBs are designed and applied to image coding. Comparing the results with conventional lossy-to-lossless image coding structures, including the 5/3- and 9/7-tap discrete wavelet transforms in JPEG 2000 and a 4 × 8 hierarchical lapped biorthogonal transform in JPEG XR, the proposed BOFBs achieve better result in both objective measure and perceptual visual quality for the images with a lot of high-frequency components.

Integer lapped orthogonal transforms (LOTs) are vital technologies for the unification of lossless and lossy image coding, called lossless to-lossy image coding. In this paper, we present an efficient realization of integer fast LOT (FLOT) based on direct-lifting of discrete cosine transforms (DCTs) which are type-II, III and IV. Although the conventional integer FLOTs suffer from degradation of coding performance due to much rounding error generated by cascading lifting structures, this paper presents a realization of a simpler, faster and more efficient transform with only some adders, 1-bit shifters and direct use of DCTs for lifting coefficients. As result, the proposed method is validated in lossless-to-lossy image coding.

In this paper, we propose a two dimensional (2D) non-separable adaptive directional lifting (ADL) structure of discrete wavelet trans form (DWT) and its image coding application. Conventionally, we have proposed a polyphase representation of a 2D non-separable lifting structure of DWT. We generalize the polyphase representation in this paper and one structure of the class has been proven to reduce errors due to the rounding operations and improve a compatibility of the irreversible 9/7 DWT, compared with a 2D separable lifting structure of DWT. Adding the adaptive directional transforming property to the generalized structure, our proposed method improves the lossy image coding performance with maintaining the compatibility.

A block-lifting factorization of M-channel biorthogonal filter banks (BOFBs) with degree-N building blocks and even/odd M (M ≥ 2) for lossless-to-lossy image coding is introduced in this paper. In the previous work, block-lifting factorization of M-channel BOFBs has been proposed. Since the block-lifting structure does not require the restriction of determinant of each building block, it achieves better coding performance than the conventional methods. However, the factorization is not completed because McMillan degree in each building block is fixed M/2 (M is even). This paper proposes a block-lifting factorization without restrictions for a fixed degree and even block size. Our proposal is validated by several filter designs and their application to lossless-to-lossy image coding.

Some adaptive image interpolation methods have been proposed to create higher visual quality images than traditional interpolation methods such as bicubic interpolation. These methods, however, often suffer from high computational costs and unnatural texture interpolation. This paper proposes a novel edge-adaptive image interpolation method using an edge-directed smoothness filter. Our approach estimates the enlarged image from the original image based on an observation model. The estimated image is constrained to have many edge-directed smooth pixels which are measured by using the edge-directed smoothness filter introduced in this paper. Simulation results show that the proposal method produces images with higher visual quality, higher PSNRs and faster computational times than the conventional methods.

A discrete cosine transform (DCT) can be easily implemented in software and hardware for the JPEG and MPEG formats. Recently, some integer DCTs (IntDCTs) for lossless-to-lossy image coding have been proposed, but they do not satisfy enough compatibility with JPEG standard. This paper proposes a realization of lossless-to-lossy image coding which has higher compatibility with it than the conventional IntDCTs. Our IntDCT is implemented by direct-lifting of DCT and inverse DCT (IDCT) and has high performance in lossless image coding compared with any IntDCT while keeping high compatibility with JPEG standard. Finally, our method is validated by its application to lossless-to-lossy image coding.

This paper presents an IntDCT with only dyadic values such as k/2n(k, n ∈ N). Although some IntDCTs have been proposed, they are unsuitable for lossless-to-lossy image coding in low-bit-word-length (coefficients). First, the proposed M-channel lossless WHT (LWHT) can be constructed by only (log2M)-bit-word-length and has structural regularity. Then, our 8-channel IntDCT keeps good coding performance even In low-bit-word-length because LWHT, which is main part of IntDCT, can be implemented by 3-bit-word-length. Finally, our method is validated In lossless-to-lossy image coding.

Adaptive directional wavelet transform is an effective alternative of the traditional 2-D wavelet transform for image coding. It is able to transform an image adaptively along diagonal orientations as well as conventional vertical/horizontal directions. However, it requires to transmit transform direction information to the decoder side. For image coding at very low bitrates, the bit budget of the direction information degrades a reconstructed image quality. In this paper, a method to construct a scalable bitstream for transform directions is presented. We utilize the fact that the matrix yielded by transform direction indices still contains the original image characteristics. The matrix is transformed by a block-lifting based DCT, then encoded by SPIHT to yield a scalable bitstream. Our method is effective for very low bitrate image coding, and is comparable to the non-scalable one for middle-to-high bitrates.

A discrete cosine transform (DCT) can be easily implemented in software and hardware for the JPEG and MPEG formats. However, even though some integer DCTs (IntDCTs) for lossless-to-lossy image coding have been proposed, such transform requires redesigned devices. This paper proposes a hardware-friendly IntDCT that can be applied to both lossless and lossy coding. Our IntDCT is implemented by direct-lifting of DCT and inverse DCT (IDCT). Consequently, any existing DCT device can be directly applied to every lifting block. Although our method requires a small side information block (SIB), it is validated by its application to lossless-to-lossy image coding.