Image reconstruction using entropy, relative entropy, and the discrete cosine transform

With advancement of technology, the image processing techniques play an important role. Image processing is required to improve the pictorial information for human perception and for autonomous machine applications. It finds application in various fields such as quality control, remote sensing, imaging science, etc. It also finds application in areas where efficient storage and transmission of images is necessary, Say for example; we want to store an image in the computer with less disk space. Also, in cases where we want to signal an image or video on a transmission medium with less bandwidth communication channel. Images are usually in the form of matrices and an uncompressed image uses huge number of bytes for storage. Image compression is used to reduce the size of the bitmap without compromising on the quality of an image. This enables to store large number of images in the same given amount of storage space. Image compression will also reduce the time taken to transmit or to download images from the internet. Many methods are available to compress an image file. The image compression methods which have gained popularity are the transform based coding methods like Discrete Cosine Transform (DCT), discrete wavelet Transform (DWT) and fractals. However these methods have drawbacks like low compression ratio and high encoding time. In this paper a new hybrid methodology is proposed by combining lossy and lossless compression methods. The proposed hybrid technique combines DCT and fractal quadtree decomposition with Huffman encoding of threshold value 0.2. The results obtained from the proposed method are then compared with state-of-the-art compression methods.

The discrete cosine transform (DCT) offers superior energy compaction properties for a large class of functions and has been employed as a standard tool in many signal and image processing applications. However, it suffers from spurious behavior in the vicinity of edge discontinuities in piecewise smooth signals. To leverage the sparse representation provided by the DCT, in this article, we derive a framework for the inverse polynomial reconstruction in the DCT expansion. It yields the expansion of a piecewise smooth signal in terms of polynomial coefficients, obtained from the DCT representation of the same signal. Taking advantage of this framework, we show that it is feasible to recover piecewise smooth signals from a relatively small number of DCT coefficients with high accuracy. Furthermore, automatic methods based on minimum description length principle and cross-validation are devised to select the polynomial orders, as a requirement of the inverse polynomial reconstruction method in practical applications. The developed framework can considerably enhance the performance of the DCT in sparse representation of piecewise smooth signals. Numerical results show that denoising and image approximation algorithms based on the proposed framework indicate significant improvements over wavelet counterparts for this class of signals.

Aim and Objective:The objective of this study was to optimize the threshold for discrete cosine transform (DCT) coefficients for near-lossless compression of Tc-99 m Dimercaptosuccinic acid (DMSA) scan images using discrete cosine transformation.Materials and Methods:Two nuclear medicine (NM) Physicians after reviewing several Tc-99 m DMSA scan images provided 242 Tc-99 m DMSA scan images that had scar. These Digital imaging and communication in medicine (DICOM) images were converted in the Portable Network Graphics (PNG) format. DCT was applied on these PNG images, which resulted in DCT coefficients corresponding to each pixel of the image. Four different thresholds equal to 5, 10, 15, and 20 were applied and then inverse discrete cosine transformation was applied to get the compressed Tc-99 m DMSA scan images. Compression factor was calculated as the ratio of the number of nonzero elements after thresholding DCT coefficients to the number of nonzero elements before thresholding DCT coefficients. Two NM physicians who had provided the input images visually compared the compressed images with its input image, and categorized the compressed images as either acceptable or unacceptable. The quality of compressed images was also assessed objectively using the following eight image quality metrics: perception-based image quality evaluator, structural similarity index measure (SSIM), multiSSIM, feature similarity indexing method, blur, global contrast factor, contrast per pixel, and brightness. Pairwise Wilcoxon signed-rank sum tests were applied to find the statistically significant difference between the value of image quality metrics of the compressed images obtained at different thresholds and the value of the image quality metrics of its input images at the level of significance = 0.05.Results:At threshold 5, (1) all compressed images (242 out of 242 Tc-99 m DMSA scan images) were acceptable to both the NM Physicians, (2) Compressed image looks identical to its original image and no loss of clinical details was noticed in compressed images, (3) Up to 96.65% compression (average compression: 82.92%) was observed, and (4) Result of objective assessment supported the visual assessment. The quality of compressed images at thresholds 10, 15, and 20 was significantly better than that of input images at P < 0.0001. However, the number of unacceptable compressed images at thresholds 10, 15, and 20 was 6, 38, and 70, respectively.Conclusions:Up to 96.65%, near-losses compression of Tc-99 m DMSA images was found using DCT by thresholding DCT coefficients at a threshold value equal to 5.

We present an extension to Jaynes’ maximum entropy principle that incorporates latent variables. The principle oflatent maximum entropywe propose is different from both Jaynes’ maximum entropy principle and maximum likelihood estimation, but can yield better estimates in the presence of hidden variables and limited training data. We first show that solving for a latent maximum entropy model poses a hard nonlinear constrained optimization problem in general. However, we then show that feasible solutions to this problem can be obtained efficiently for the special case of log-linear models---which forms the basis for an efficient approximation to the latent maximum entropy principle. We derive an algorithm that combines expectation-maximization with iterative scaling to produce feasible log-linear solutions. This algorithm can be interpreted as an alternating minimization algorithm in the information divergence, and reveals an intimate connection between the latent maximum entropy and maximum likelihood principles. To select a final model, we generate a series of feasible candidates, calculate the entropy of each, and choose the model that attains the highest entropy. Our experimental results show that estimation based on the latent maximum entropy principle generally gives better results than maximum likelihood when estimating latent variable models on small observed data samples.

A lot of attentions has been paid by the researchers for lossy image compression. Due to the high uses of multimedia, a high image compression ratio while keeping good image quality, is still a research issue. In this paper, we proposed an image compression using adaptive scanning, in which DWT(discrete wavelet transform) is performed to source image, DCT(discrete cosine transform) is performed to obtained DWT elements. Next, non zero quantized DCT (discrete cosine transform) coefficients are represented in less number of bits. First, the source image is divided into \(16\times 16\) grids and then DWT transformed, later the obtained elements are divided into \(8\times 8\) grids and then DCT is performed, quantized, differential encoded and an indexed vector is formed from the quantized matrix using adaptive scanning. Furthermore the indexed vector is divided into two indexed vectors namely \(nonzero\) vector and zerocount vector. The nonzero coefficients are stored in \(nonzero\) vector and the number of zeros preceding a nonzero coefficient is stored in zerocount vector. A new block is introduced to store the number of bits required to store highest value of nonzero coefficient in \(nonzero\) vector so that all the nonzero elements can be represented in that many bits rather than a fixed number of bits. The experimental results show that the proposed method has achieved more compression ratio with slight reduction in image quality as compared to existing recent methods.

Traffic congestion has always been a major problem in the Philippines. This project study developed an integrated sensor system for intelligent transportation, which addressed the lack of automatic traffic monitoring systems to achieve traffic efficiency and safety. The researchers utilized different sensors in gathering data such as water level, temperature, and humidity within a certain area as well as a camera in capturing images and compared the three image compression algorithms, mainly the DCT (Discrete Cosine Transform), DWT (Discrete Wavelet Transform) and SVD (singular value decomposition) in terms of different parameters used in describing and identifying the best type of image compression to be applied prior to transmission to other different nodes. MSE (mean squared error) value, PSNR (Peak signal-to-noise ratio), Compress Ratio, and Process Time were the values of comparison in determining the best compression technique or algorithm for the gathered images. As a result, it was found that DCT characterized the best parameters for image compression. DCT produced the highest PSNR (52.41979dB), the lowest value for MSE (0.37247), and the lowest process time (0.16181s), while SVD was able to produce the most compressed image. This project also utilized solar renewable energy for the power management system, which enabled the system to run independently without any other external power source. This will be beneficial for the community to identify which roads can be used to optimize the mobility of the vehicles and maximize the use of renewable energy; hence will help reduce the traffic congestion issues in the country.

Objective: The purpose of this work is to present the experimental results by comparing the quality of different satellite images LANDSAT 7, MODIS and ASTER after compression, using four different compression methods. Methods/Analysis: The satellite images are compressed using four different basic compression methods namely, Pulse code Modulation, Differential Pulse Code Modulation, Discrete Cosine Transform and Sub band Coding. The Compression is performed with three different types of satellite sensor images having different spectral bands, picture bit-rate and level of details using VCDemo software package. Findings: The Mean Square Error, Signal to Noise Ratio and Peak Signal to Noise Ratio values are calculated to determine the quality of the images after compression. In order to find the quality of compression methods the Mean Square Error, Signal to Noise Ratio and Peak Signal to Noise Ratio values are collected for different satellite images by compressing with different bitrates. While comparing the obtained values for each compression methods, we found that the compression methods have different impacts in each satellite image according to the bit-rate used for compression and the level of details. Conclusion: The study proves that Discrete Cosine Transform and Sub band Coding’s performance are worthy for satellite image compression. Where Sub band Coding produces a very good Signal to Noise Ratio and Peak Signal to Noise Ratio values for all bit rates. Keywords: DCT, Image Compression, MSE, PSNR, Satellite Image Compression, SBC, SNR

The set of solutions inferred by the generic maximum entropy (MaxEnt) or maximum relative entropy (MaxREnt) principles of Jaynes - considered as a function of the moment constraints or their conjugate Lagrangian multipliers - is endowed with a Riemannian geometric description, based on the second differential tensor of the entropy or its Legendre transform (negative Massieu function). The analysis provides a generalised {\it least action bound} applicable to all Jaynesian systems, which provides a lower bound to the cost (in generic entropy units) of a transition between inferred positions along a specified path, at specified rates of change of the control parameters. The analysis therefore extends the concepts of "finite time thermodynamics" to the generic Jaynes domain, providing a link between purely static (stationary) inferred positions of a system, and dynamic transitions between these positions (as a function of time or some other coordinate). If the path is unspecified, the analysis gives an absolute lower bound for the cost of the transition, corresponding to the geodesic of the Riemannian hypersurface. The analysis is applied to (i) an equilibrium thermodynamic system subject to mean internal energy and volume constraints, and (ii) a flow system at steady state, subject to constraints on the mean heat, mass and momentum fluxes and chemical reaction rates. The first example recovers the {\it minimum entropy cost} of a transition between equilibrium positions, a widely used result of finite-time thermodynamics. The second example leads to a new {\it minimum entropy production principle}, for the cost of a transition between steady state positions of a flow system.

Transform coding has been the focus of the research for image compression. In previous research, the Amplitude and Group Partitioning (AGP) coding scheme is proved to be a low complexity algorithm with higher performance, clearly one of the state-of-art transform coding techniques. However, the previous AGP is used along with the Discrete Cosine Transform (DCT) and the discrete wavelet transform. In this paper, a different transform, the Lapped Orthogonal Transform (LOT), replaces the DCT in conjunction with the AGP. This is the first time LOT and AGP have been combined in a coding method. The definition and design of the LOT are discussed. An objective metric to measure the performance of transform, coding gain, is calculated for both the DCT and the LOT. The LOT has slightly higher coding gain than the DCT. The principles of the LOT based AGP image codec (LOT-AGP) are presented and a complete codec, encoder and decoder, is implemented in software. The performance of the LOT-AGP is compared with other block transform coding schemes: the baseline JPEG codec and the DCT based AGP image codec (DCT- AGP) by both objective evaluation and subjective evaluation. The Peak Signal to Noise Ratio (PSNR) is calculated for these three coding schemes. The two AGP codecs are much better than the JPEG codec on PSNR, from about 1.7 dB to 3 dB depending on bit rate. The two AGP schemes have PSNR differences only to a small degree. Visually, the LOT-AGP has the best-reconstructed images among these three at all bit rates. In addition, the coding results of two other state-of-art progressive image codecs are cited for further comparison. One is the Set Partitioning in Hierarchical Trees (SPIHT) algorithm with a dyadic wavelet transform, and the other is Tran and Nguyen's method with the generalized LOT transform. The AGP coding and the adaptive Huffman entropy coding of LOT-AGP are less complex and the memory usage is smaller than in these two progressive codecs. Comparing these three codecs, i.e. the LOT-AGP and the two progressive codecs in PSNR small only small differences in PSNR. SPIHT has about 1 dB higher PSNR than the LOT-AGP and Tran and Nguyen's method for the test image Lena. For the test image Barbara, the PSNR of the LOT- AGP is about 0.5 dB higher than that of the SPIHT and 0.5 dB lower than that of Tran and Nguyen's method. This low- complexity and high performance codec may provide a new direction for the implementation of image compression.

Discrete transforms play an important role in digital signal processing. In particular, due to its transform domain energy compaction properties, the discrete cosine transform (DCT) is pivotal in many image processing problems. This paper introduces a numerical approximation method for the DCT based on round-off techniques. The proposed method is a multiplierless technique with low arithmetic complexity. Emphasis was given to approximating the 8-point DCT. A fast algorithm for the introduced 8-point approximate transform was derived. An application in image compression was examined. In several scenarios, the utilization of the proposed method for image compression resulted in comparable or better performances, when compared to the usual DCT-based methodology.

It is already known that a curve estimated via the discrete cosine transform (DCT) always passes through all the measured points without using imaginary numbers in the DCT coefficients, unlike the discrete Fourier transform. Moreover, owing to its character, the DCT can be used instead of the nonlinear least-squares method to express various theoretical curves. Because the DCT is a kind of Fourier transform, there is a possibility that the DCT could be employed to draw electron density distribution maps of crystals. If so, the probability that the DCT could be used to investigate the internal structure of materials by analysing the theoretical curves would increase. This article reports an attempt to draw the electron density distribution maps of the Mg3BN3 low-pressure phase [Mg3BN3(L)] by using the DCT in order to confirm the utility of the DCT for analysing the internal structure of materials. It is found that the DCT can provide mirror-symmetric electron density distribution projection maps and a modified DCT can be used to calculate whole standard electron density distribution projection maps for the surface plane of the unit cell. Moreover, a real crystal structure that has a centre of symmetry can be determined by the DCT by transforming a 1/4 part of the mirror-symmetric electron density distribution projection map.

Discrete Cosine Transform (DCT) has an important role in image compression. This paper presents a fast 2D-DCT architecture for hardware efficient embedded systems and power limited applications such as Internet of Things (IoT). The proposed design both from a structure point of view and operation reduction point of view has two headed approaches toward the problem of image and video compression. It includes a modified high speed architecture using an extra operational reducing technique. Reduction of operations occurs in two stages while computing 8-point DCT transform of the blocks. Defining the appropriate threshold for comparing DCT domain of two rows of an 8*8 block. Approximating DCT operations column-wise is the additional approach of the paper. The architecture is implemented on Xilinx Vivado 2018.2 with VHDL language on Artix-7 FPGA. 207 MHz clock frequency has achieved.

The study aims to develop a measurement system for acquiring ultrasonic transmission tomography data. Along building the automated measurement system we test the algorithm which use incorporation of image compression into the process of reconstruction what speed up computation and simplifies regularization of the solution to the inverse problem of tomography. The reconstructive algorithm used in transmission tomography is based on the Discrete Cosine Transformation method. The algorithm applies image compression techniques for each block of the image separately, according to the conducted test such a solution seems to be much more robust than classical methods used for ultrasonic tomography. Presented work is a part of the research that aim for applying ultrasonic technology for analyse and visualise technological processes in distributed systems and in the next step for development of wearable equipment for monitoring in medicine.

Transmitting images over an Orthogonal Frequency Division Multiplexing Access (OFDMA) system poses a significant challenge. The process entails sending a substantial amount of data, which consumes a significant amount of bandwidth. Consequently, compressing the transmitted image becomes essential to reduce the required bandwidth. The aim of this paper is to examine and analyse the wireless transmission of a compressed image via Discrete Cosine Transform (DCT‐OFDMA). A comparison is made with Discrete Fourier Transform (DFT‐OFDMA), across various subcarrier mapping schemes (localized and inter‐leaved), and different modulation schemes (16 Quadrature Amplitude Modulation (16QAM) and Quadrature Phase Shift Keying (QPSK)) using vehicular A, Stanford University Interim (SUI3), and uniform channel models. To evaluate the performance of the system, the minimum Signal‐to‐Noise Ratio (SNR) necessary to recover the transmitted compressed image is calculated. This work considers nine standard compression techniques. The results are carried out using the MATLAB simulator. According to the simulation results, the minimum SNR required to recover the transmitted compressed image was found to be 19 dB. This result was achieved when using Discrete Cosine Transform‐Loaclized‐Orthogonal Frequency Division Multiplexing Access (DCT‐LOFDMA) with QPSK modulation and set partitioning in hierarchical trees (SPIHT) compression method over the SUI3 channel model. Moreover, it was observed that the DCT‐LOFDMA and DFT‐IOFDMA systems attained equal SNR while utilizing the SPIHT_3D compression technique and QPSK modulation on the SUI3 channel model. Overall, the results suggest that the performance of DCT‐based localized OFDMA is somewhat superior to DFT‐based localized OFDMA, particularly when utilizing the SUI3 channel model and the QPSK modulation scheme. Therefore, it is feasible to transmit and receive a compressed image effectively over an OFDMA system with DCT.

A hybrid compression method for the NMR data based on window averaging and Discrete Cosine Transform