Conventional Discrete Cosine Transform Research Articles

Graph Based Cross-Channel Transform for Color Image Compression

Adaptive transform coding is gaining more and more attention for better mining of image content over fixed transforms such as discrete cosine transform (DCT). As a special case, graph transform learning establishes a novel paradigm for the graph-based transforms. However, there still exists a challenge for graph transform learning-based image codecs design on natural image compression, and graph representation cannot describe regular image samples well over graph-structured data. Therefore, in this article, we propose a cross-channel graph-based transform (CCGBT) for natural color image compression. We observe that neighboring pixels having similar intensities should have similar values in the chroma channels, which means that the prominent structure of the luminance channel is related to the contours of the chrominance channels. A collaborative design of the learned graphs and their corresponding distinctive transforms lies in the assumption that a sufficiently small block can be considered smooth, meanwhile, guaranteeing the compression of the luma and chroma signals at the cost of a small overhead for coding the description of the designed luma graph. In addition, a color image compression framework based on the CCGBT is designed for comparing DCT on the classic JPEG codec. The proposed method benefits from its flexible transform block design on arbitrary sizes to exploit image content better than the fixed transform. The experimental results show that the unified graph-based transform outperforms conventional DCT, while close to discrete wavelet transform on JPEG2000 at high bit-rates.

Geometric deviation modeling for single surface tolerancing using Laplace-Beltrami Operator

ISO standards on geometrical product specifications and verification (GPS) categorize the geometrical features partitioned from shapes based on their kinematic invariance classes. As a key issue to achieve predictable and interchangeable shape, geometrical tolerancing defines the tolerance zone within which the partitioned features shall be contained for dimensional and geometrical accuracy. However, most of the current research activities consider the geometrical features as orientation and position deviations of substitute ideal surfaces and neglect form errors within the developed models. In order to enhance the tolerance analysis and simulation, the concept of Skin Model Shapes (SMS) is therefore proposed to represent surface deviations in accordance with random nature of geometric deviations. In this paper, a new approach based on spectral analysis is proposed for SMS generation on mechanical parts. The Eigen-system of Laplace-Beltrami Operator (LBO) enables shape analysis with an unambiguous mathematical language due to its invariance of the position and orientation. The SMS generation process is completed with LBO by developing a modeling methodology for geometric deviation representation and generation on single surfaces in the design process. The obtained spatial frequency LBO decomposition on the single surface of invariant class is used to represent the statistical characteristics of the deviations and further used to reproduce deviations with similar distributions. A comparison is presented in the paper to illustrate the difference between a conventional Discrete Cosine Transform (DCT) based method and the proposed LBO-based method. Another case study is investigated to explain the implementation of the proposed method on different types of single surfaces of invariant class generation based on SMS.

Comparative Analysis of an Efficient Image Denoising Method for Wireless Multimedia Sensor Network Images in Transform Domain

In recent years, there has been an increasing research interest in image de-noising due to an emphasis on sparse representation. When sparse representation theory is compared to transform domain-based image de-noising, the former indicates that the images have more information. It contains structural characteristics that are quite similar to the structure of dictionary-based atoms. This structure and the dictionary-based method is highly unsuccessful. However, image representation assumes that the noise lack such a feature. The dual-tree complex wavelet transform incorporates an increase in transform data density to reduce the effects of sparse data. This technique has been developed to decrease the image noise by selecting the best-predicted threshold value derived from wavelet coefficients. For our experiment, Discrete Cosine Transform (DCT) and Complex Wavelet Transform (CWT) are used to examine how the suggested technique compares the conventional DCT and CWT on sets of realistic images. As for image quality measures, DT-CWT has leveraged superior results. In terms of processing time, DT-CWT gave better results with a wider PSNR range. Further, the proposed model is tested with a standard digital image named Lena and multimedia sensor images for the denoising algorithm. The suggested denoising technique has delivered minimal effect on the MSE value.

Secure compressive sensing of images based on combined chaotic DWT sparse basis and chaotic DCT measurement matrix

In this paper, secure compressive sensing based on a combination of the chaotic discrete wavelet transform (DWT) basis and chaotic discrete cosine transform (DCT) measurement matrix is proposed. In the proposed scheme, a logistic map is employed to generate two chaotic sequences that are used to scramble the rows of the conventional DCT and original DWT matrix to form a chaotic measurement matrix and sparse basis matrix, respectively. The original image is first transformed into a sparse domain signal by the obtained chaotic DWT matrix. Thereafter, the resulting signal is compressively sampled by the obtained chaotic DCT measurement matrix. Numerical experiments show that the proposed scheme not only achieves image encryption and compression simultaneously but also enlarges the key space and improves the quality of the reconstructed image compared to that of the conventional chaotic measurement matrix method.

Investigations on wavelet and Fourier transform based channel estimation in MIMO-OFDM system

In this paper channel estimation methods for MIMO-OFDM system are investigated based on Fourier Transform and Wavelet Transform. The channel estimation algorithm based on Discrete Fourier Transform (DFT) cause energy leakage in multipath channel with non-sample-spaced time delays. Discrete Cosine Transform (DCT) based channel estimator can mitigate the drawback of Discrete Fourier Transform based channel estimator, when the non-sample spaced path delays are available in multipath fading channels. Wavelet based systems provide better spectral efficiency because of no cyclic prefix requirement, with narrow side lobes and also exhibit improved BER performance. Simulation results reveal that the DWT based transform outperforms the conventional DFT and DCT based channel estimator in terms of bit error rate and mean square error.

Enhanced Configurable DCT Cordic Loeffler Architectures for Optimal Power-PSNR Trade-Off

The Discrete Cosine Transform (DCT) is one of the most widely used techniques of transforms in digital signal processing. It is the main algorithm in image and video coding systems. In this paper, we propose an algorithm which generates enhanced Cordic based Loeffler DCT architectures for angle’s precision degrees ranging from 10−1 to 10−7. High level PSNR, area and power estimators have been proposed to make a trade-off between consumption and image quality. An optimal architecture has been retained for its low complexity, low power and high PSNR. The complexity of this architecture is the lowest among the conventional DCT architectures even the BinDCT which is a reference in terms of reduced complexity. The selected architecture has also the closest PSNR to the reference Loeffler-DCT architecture without a substancial loss of power.

An Approach to Image Compression by Using Sparse Approximation Technique

Abstract Image compression has been a widely researched field for decades. Recently, there has been a growing interest in using basis selection algorithms for signal approximation and compression. Signal approximation using a linear combination of basis from an over-complete dictionary has proven to be an NP-hard problem. By selecting a smaller number of basis than the span of the signal, we achieve glossy compression in exchange for a small reconstruction error. For the past few decades orthogonal and bi-orthogonal complete dictionaries such as Discrete Cosine Transform (DCT) or wavelets were the dominant transform domain representations of signals. Over-complete dictionaries have been intensively studied and successfully applied to various application such as image de-noising, compression etc. The DCT and wavelet based compression methods suffer from blocking and ringing artefacts and also they are unable to capture the directional information. So, in this context an investigation has been made by using sparse coding method by Orthogonal Matching Pursuit (OMP) algorithm. In this proposed work, conventional DCT can be replaced by a set of trained dictionaries. For dictionary construction we have used a combination of DCT and Gabor basis and to encode the trained dictionary elements we have employed OMP algorithm. Experimental results demonstrate that the proposed method provides gains in Rate Distortion (RD) performance and improvements in perceptual quality.

A Scaling Scheme for DCT Precoded Optical Intensity-Modulated Direct Detection Systems

A scaling technique is employed to improve the performance of a Discrete Cosine Transform (DCT) precoded optical intensity-modulated direct detection (IM/DD) OFDM system, which fully exploits the dynamic range of a digital-to-analog converter (DAC). The theoretical analysis shows that the proposed scaling scheme can improve the BER performance of DCT precoded and scaled OFDM systems. The experiment results also show that the proposed scheme significantly improves the BER performance without changing the receiver structure. The measured received sensitivity at a BER of 10−3for a 4 G samples/s (2.7 Gbits/s) DCT precoded and scaled OFDM signal and after 100 km standard single-mode fiber (SMF) transmission has been improved by 3 and 1.3 dB when compared with the original OFDM system and conventional DCT precoded OFDM system, respectively.

Windowed All Phase Biorthogonal Transform and Its Application in JPEG-Like Image Compression

This paper proposes new concepts of the windowed all phase biorthogonal transform (WAPBT), which is inspired by the all phase biorthogonal transform (APBT). In the light of windowed all phase digital filter theory, windowed all phase biorthogonal transforms is proposed. The matrices of WAPBT based on DFT, WHT, DCT and IDCT are deduced, which can be used in image compression instead of the conventional DCT, and the image compression scheme proposed in this paper is called WAPBT-based JPEG (WAPBT-JPEG). With optimal window sequence of WAPBT for image compression obtained by using generalized pattern search algorithm (GPSA), the peak signal to noise ratio (PSNR) and visual quality of the reconstructed images using the WAPBT-JPEG is outgoing DCT-based JPEG (DCT-JPEG) and APBT-based JPEG (APBT- JPEG) approximately at all bit rates. What is more, by comparison with DCT-JPEG, the advantage of proposed scheme is that the quantization table is simplified and the transform coefficients can be quantized uniformly. Therefore, the computing time becomes shorter and the hardware implementation is easier. Index Terms—Windowed all phase biorthogonal transform (WAPBT), image compression, discrete cosine transform (DCT), JPEG algorithm, generalized pattern search algorithm (GPSA), windowed all phase digital filter (APDF)

A Discrete Fractional Cosine Transform Based Speech Enhancement System Through Adaptive Kalman Filter Combined with Perceptual Weighting Filter with Pitch Synchronous Analysis

The speech enhancement plays a vital role commonly used in noisy environment to develop the performance of speech identification in mobile phones or in car navigation system. Thus the quality of the performance of the speech recognition is becoming worse due to the presence of noises in the surrounding. The objective is to increase the evident quality of the speech and to develop the transparency. Signal representation and enhancement in cosine transformation is observed to provide significant results. As an alternative of using DCT, a combination of conventional Discrete Cosine Transform (DCT) and Discrete Fourier Transform (DFT) which forms the another transform called as the Discrete Fractional Cosine Transform (DFrCT). The DFrCT have a free parameter, its fraction. In order to deal with the issue of frame to frame deviations of the Cosine Transformations, DFrCT is integrated with Pitch Synchronous Analysis (PSA). Also Pitch Synchronous OverLap and Add (PSOLA) method are used to enhance the performance of PSA. Moreover, in order to improve the noise minimization of the system, Improved Iterative Wiener Filtering approach called Adaptive Kalman Filter Combined with Perceptual Weighting Filter is used in this approach. This filter is used to eliminate the matrix operations, reduces both the calculation time and complexity. Thus, a novel DFrCT based speech enhancement using improved iterative filtering algorithm integrated with PSA is used in this approach

Low-complex energy-aware image communication in visual sensor networks

A low-complex, low bit rate, energy-efficient image compression algorithm explicitly designed for resource-constrained visual sensor networks applied for surveillance, battle field, habitat monitoring, etc. is presented, where voluminous amount of image data has to be communicated over a bandwidth-limited wireless medium. The proposed method overcomes the energy limitation of individual nodes and is investigated in terms of image quality, entropy, processing time, overall energy consumption, and system lifetime. This algorithm is highly energy efficient and extremely fast since it applies energy-aware zonal binary discrete cosine transform (DCT) that computes only the few required significant coefficients and codes them using enhanced complementary Golomb Rice code without using any floating point operations. Experiments are performed using the Atmel Atmega128 and MSP430 processors to measure the resultant energy savings. Simulation results show that the proposed energy-aware fast zonal transform consumes only 0.3% of energy needed by conventional DCT. This algorithm consumes only 6% of energy needed by Independent JPEG Group (fast) version, and it suits for embedded systems requiring low power consumption. The proposed scheme is unique since it significantly enhances the lifetime of the camera sensor node and the network without any need for distributed processing as was traditionally required in existing algorithms.

FPGA implementation of a novel DCT architecture reducing constant cosine terms

This paper presents a new scalable architecture for Discrete Cosine Transform (DCT). In contrast to the conventional DCT architecture, the proposed architecture reduces the number of constant cosine terms using the matrix transposition and symmetry property. This in turn, considerably reduces the computation time. The architecture is scalable and it can be extended to support any transform length. The architecture was validated on Xilinx Vertex-4 FPGA.

Video Coding With Rate-Distortion Optimized Transform

Block-based discrete cosine transform (DCT) has been successfully adopted into several international image/video coding standards, e.g., MPEG-2, H.264/AVC, as it can achieve a good tradeoff between performance and complexity. Although DCT theoretically approximates the optimum Karhunen-Loeve transform under first-order Markov conditions, one fixed set of transform basis functions (TBF) cannot handle all the cases efficiently due to the non-stationary nature of video contents. To further improve the performance of block-based transform coding, in this paper, we present the design of rate-distortion optimized transform (RDOT) which contributes to both intraframe and interframe coding. The most important property which makes a difference between RDOT and the conventional DCT is that, in the proposed method, transform is implemented with multiple TBF candidates which are obtained from off-line training. With this feature, for coding each residual block, the encoder is capable to select the optimal set of TBF in terms of rate-distortion performance, and better energy compaction is achieved in the transform domain. To obtain an optimum group of candidate TBF, we have developed a two-step iterative optimization technique for the off-line training, with which the TBF candidates are refined at each iteration until the training process becomes converged. Moreover, analysis on the optimal group of candidate TBF is also presented in this paper, with a detailed description of a practical implementation for the proposed algorithm on the latest VCEG key technical area software platform. Extensive experimental results show that, compared with the conventional DCT-based transform scheme adopted into the state-of-the-art H.264/AVC video coding standard, significant improvement of coding performance has been achieved for both intraframe and interframe coding with our proposed method.

Zeros Removal with DCT Image Compression Technique

The discrete cosine transform (DCT) is a method for converting a signal into plain frequency components. It is extensively used in image compression. In this paper a new technique is proposed, namely ZRDCT (Zeros Removal with DCT) which is based on a lossy compression, and used to enhance image data compression.Image quality is measured impartially, using peak signal-to-noise ratio (PSNR) or picture quality scale, and individually using perceived image quality with compression factor (CF) being the main theme of this paper, taking into consideration the preservation of well PSNR outputs. The performance of DCT compression generally degrades low bit-rates mainly because of the underlying block-based DCT scheme. Experimental results demonstrated the effectiveness of the ZRDCT approach, which enhanced the performance of the conventional DCT image compression methods, by investigating and interrogating the whole image and hence enforcing mechanisms for finding possible redundant information and therefore the removal of unnecessary data which lead to an improvement in CF without upsetting PSNR.The new technique also proved to have low distortions with good quality PSNR, commendable CF and good execution time, when compared to other various DCT schemes and with some wavelet based image compression

All phase biorthogonal transform and its application in JPEG-like image compression

This paper proposes new concepts of the all phase biorthogonal transform (APBT) and the dual biorthogonal basis vectors. In the light of all phase digital filtering theory, three kinds of all phase biorthogonal transforms based on the Walsh transform (WT), the discrete cosine transform (DCT) and the inverse discrete cosine transform (IDCT) are proposed. The matrices of APBT based on WT, DCT and IDCT are deduced, which can be used in image compression instead of the conventional DCT. Compared with DCT-based JPEG (DCT-JPEG) image compression algorithm at the same bit rates, the PSNR and visual quality of the reconstructed images using these transforms are approximate to DCT, outgoing DCT-JPEG at low bit rates especially. But the advantage is that the quantization table is simplified and the transform coefficients can be quantized uniformly. Therefore, the computing time becomes shorter and the hardware implementation easier.

Directional Discrete Cosine Transforms—A New Framework for Image Coding

Nearly all block-based transform schemes for image and video coding developed so far choose the 2-D discrete cosine transform (DCT) of a square block shape. With almost no exception, this conventional DCT is implemented separately through two 1-D transforms, one along the vertical direction and another along the horizontal direction. In this paper, we develop a new block-based DCT framework in which the first transform may choose to follow a direction other than the vertical or horizontal one. The coefficients produced by all directional transforms in the first step are arranged appropriately so that the second transform can be applied to the coefficients that are best aligned with each other. Compared with the conventional DCT, the resulting directional DCT framework is able to provide a better coding performance for image blocks that contain directional edges-a popular scenario in many image signals. By choosing the best from all directional DCTs (including the conventional DCT as a special case) for each image block, we will demonstrate that the rate-distortion coding performance can be improved remarkably. Finally, a brief theoretical analysis is presented to justify why certain coding gain (over the conventional DCT) results from this directional framework.

Lifting-Based Directional DCT-Like Transform for Image Coding

Traditional 2-D discrete cosine transform (DCT) implemented by separable 1-D transform in horizontal and vertical directions does not take image orientation features in a local window into account. To improve it, we propose to introduce directional primary operations to the lifting-based DCT and thereby derive a new directional DCT-like transform, whose transform matrix is dependent on directional angle and interpolation used there. Furthermore, the proposed transform is compared with the straightforward one of first rotated and then transformed. A JPEG-wise image coding scheme is also proposed to evaluate the performance of the proposed directional DCT-like transform. The first 1-D transform is performed according to image orientation features, and the second 1-D transform still in the horizontal or vertical direction. At the same time, an approach is proposed to optimally select transform direction of each block because selected directions of neighboring blocks will influence each other. The experimental results show that the performance of the proposed directional DCT-like transform can dramatically outperform the conventional DCT up to 2 dB even without modifying entropy coding.

Acceleration of DCT Processing with Massive-Parallel Memory-Embedded SIMD Matrix Processor

This paper reports an efficient Discrete Cosine Transform (DCT) processing method for images using a massive-parallel memory-embedded SIMD matrix processor. The matrix-processing engine has 2,048 2-bit processing elements, which are connected by a flexible switching network, and supports 2-bit 2,048-way bit-serial and word-parallel operations with a single command. For compatibility with this matrix-processing architecture, the conventional DCT algorithm has been improved in arithmetic order and the vertical/horizontal-space 1 Dimensional (1D)-DCT processing has been further developed. Evaluation results of the matrix-engine-based DCT processing show that the necessary clock cycles per image block can be reduced by 87% in comprison to a conventional DSP architecture. The determined performances in MOPS and MOPS/mm2 are factors 8 and 5.6 better than with a conventional DSP, respectively.

Fast 2D discrete cosine transform on compressed image in restricted quadtree and shading format

Given a compressed image in the restricted quadtree and shading format, this paper presents a fast algorithm for computing 2D discrete cosine transform (DCT) on the compressed grey image directly without the need to decompress the compressed image. The proposed new DCT algorithm takes O( K 2log K+ N 2) time where the decompressed image is of size N× N and K denotes the number of nodes in the restricted quadtree. Since commonly K< N, the proposed algorithm is faster than the indirect method by decompressing the compressed image first, then applying the conventional DCT algorithm on the decompressed image. The indirect method takes O( N 2log N) time.

Mixed‐transform image coding with variable block sizes

In the proposed image coding, variable block size and two transforms are used in image transform coding. A 16×16 image block is detected to be active or inactive according to activity indexes which are the values of three transform coefficients. If the image block is active, then it is partitioned to four 8×8 image blocks and then processed by a 2‐D 8×8 discrete cosine transform (DCT); otherwise it is processed by a 2‐D 16×16 Walsh‐Hadmard transform (WHT) directly since the WHT has simple structure and the same image compression performance as the DCT does for inactive image blocks. As a result, the proposed approach is to process image blocks by a 16×16 WHT or an 8×8 DCT. If the PSNRs for both the conventional DCT image coding and the mixed‐transform coding are kept the same in our experiments with 9 images, the number of additions of the latter increases by 4.18% on average, but the number of the multiplications decreases by 78.53% at bit rate 0.5.