COMPRESSIVE SENSING BASED SIGNAL RECOVERY WITH DIFFERENT TRANSFORMS

Image encryption based on compressive sensing and chaos systems

This paper demonstrates the merits of nested Compressive Sensing (CS) approach for Electrocardiogram (ECG) signals using discrete wavelet transform (DWT) and discrete cosine transform (DCT) as sensing matrix and sparsifying matrix. The implementation of CS framework is done using Gradient Projection for Sparse Reconstruction (GPSR). It is tested on 9 ECG signals of different arrhythmia categories obtained from MITBIH and BIDMC dataset. It is analysed for 3 different combinations, case (1) DCT sensing and DWT sparsification, case (2) DWT sensing and DCT sparsification and case (3) DWT sensing and DWT sparsification. A novel hybrid nested CS approach is proposed as case (4) which is a combination of case (2) in higher level and case (1) in lower level. This nested method yields the best PRD of 1.39 for CR = 0.2 and performs better than all proposed cases. This proposed approach involves a fair method of discarding the measurements in all frequency band and performs better than the state of the art work when the sampling rate is reduced by 4 times for ECG signal 100.dat from MIT-BIH (Massachusetts Institute of Technology-Beth Israel Hospital) database for CR = 0.2. It is shown that the reconstruction time of the proposed nested CS approach is lesser than non-nested CS approach.

The transformation model plays a vital role in medical image processing. This paper proposed new two Mixed Transforms models that are the hybrid combination of linear and nonlinear Transformations techniques. The first mixed transform is computed in three steps: calculate 2D discrete cosine transform (DCT) of the image, and applying Arnold Transform (AT) on the DCT coefficients, and applying the discrete Wavelet Transform (DWT) on the result to get which was abbreviated as (CAW). The second mixed transform consists of firstly computing the discrete Fourier transform (DFT), net applying the Arnold Transform (AT), and finally, the computation of discrete Wavelet Transform (DWT) which was abbreviated as (FAW). These transforms have superior directional representations as compared to other multiresolution representations such as DWT or DCT and work as non-adaptive mixed transformations for multi-scale object analysis. Due to their relationship to the wavelet idea, they are finding increasing use in areas like image processing and scientific computing. These transforms are tested in medical image classification task and their performances are compared with that of the traditional transforms. CAW and FAW transforms are used in the feature extraction stage of a classification VGG16 deep learning (DNN) task of Tumor MRI medical image. The numerical findings favor CAW and FAW over the wavelet transform for estimating and classifying pictures. From the results obtained it was shown that the CAW and FAW transform gave e much higher classification rate than that achieved with the traditional transforms, namely DCT, DFT and DWT. Furthermore, this combination leads to a family of directional and multi-transformation bases for image processing.

Over the years, a variety of other linear transforms have been developed which include discrete Fourier transform (DFT), discrete wavelet transform (DWT) and discrete cosine transform (DCT) and many more, each with its own advantages and disadvantages. Among these techniques, DWT has been proven to be very efficient for ECG signal coding. It is proposed to develop, a hybrid two-stage ECG signal compressor based on DCT and DWT. Proposed method is hybrid ECG compression technique based on wavelet transformation of the DCT coefficients of the signal. Interaction of DCT analysis with DWT transformations, signal thresholding and coding are a few of the many outstanding challenges in ECG compression. Proposed method will offer optimized CR and PRD, which would be suitable for most monitoring and diagnostic applications. KeywordsDCT, DWT, Wavelet, Image Processing, Signal Compression.

Compressed sensing (CS) is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper, we apply the iterative hard thresholding (IHT) algorithm for compressed sensing on the speech signal. The interested speech signal is transformed to the frequency domain using Discrete Fourier Transform (DCT) and then compressed sensing is applied to that signal. The compressed signal can be reconstructed using the recently introduced Iterative Hard Thresholding (IHT) algorithm and also by the tradditional \( \ell_{1} \) minimization (basic pursuit) for comparison. It is shown that the compressed sensing can provide better root mean square error (RMSE) than the tradition DCT compression method, given the same compression ratio.

Compressed sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. It holds valuable implications for wireless sensor networks because power and bandwidth are limited resources. In this paper, applying the theory of compressed sensing to the practical sensor network data recovery problem, we compare the performance of different CS reconstruction algorithms combined with wavelet and discrete cosine transform (DCT) basis. We demonstrate empirically that DCT is good for sinusoid oscillatory data while wavelet is good for data with point-like singularities. Furthermore, comparison on reconstruction algorithms shows basis pursuit (BP) is best in term of PSNR performance and computing time. In addition, benefit of CS for noisy channel of sensor network is tested and how to achieve good performance in noisy channel is discussed.

One of the major concerns in 5G IoT networks is that most of the sensor nodes are powered through limited lifetime, which seriously affects the performance of the networks. In this article, Compressive sensing (CS) technique is used to decrease transmission cost in 5G IoT networks. Sparse basis is one of the important steps in the CS. However, most of the existing sparse basis-based method such as DCT (Discrete cosine transform) and DFT (Discrete Fourier Transform) basis do not capture data structure characteristics in the networks. They also do not take into consideration multi-resolution representations. In addition, some of sparse basis-driven methods exploit either spatial or temporal features, resulting in performance degradation of CS-based strategies. To address these challenging problems, we propose a novel spatial–temporal correlation basis algorithm (SCBA). Subsequently, an optimal basis algorithm (OBA) is provided considering greedy scoring criteria. To evaluate the efficiency of OBA, orthogonal wavelet basis algorithm (OWBA) by employing NS (Numerical Sparsity) and GI (Gini Index) sparse metrics is also presented. In addition, we discuss the complexity of the above three algorithms, and prove that OBA has low numerical rank. After experimental evaluation, we found that OBA is capable of the sparsest representing original signal compared to spatial, DCT, haar-1, haar-2, and rbio5.5. Furthermore, OBA has the low recovery error and the highest efficiency.

The main contribution of this paper is using compressive sensing (CS) theory for crypto steganography system to increase both the security and the capacity and preserve the cover image imperceptibility. For CS implementation, the discrete Cosine transform (DCT) as sparse domain and random sensing matrix as measurement domain are used. We consider 7 MRI images as the secret and 7 gray scale test images as cover. In addition, three sampling rates for CS are used. The performance of seven CS recovery algorithms in terms of image imperceptibility, achieved peak signal to noise ratio (PSNR), and the computation time are compared with other references. We showed that the proposed crypto steganography system based on CS works properly even though the secret image size is greater than the cover image.

This paper proposes a new image compression-encryption algorithm based on a meaningful image encryption framework. In block compressed sensing, the plain image is divided into blocks, and subsequently, each block is rendered sparse. The zigzag scrambling method is used to scramble pixel positions in all the blocks, and subsequently, dimension reduction is undertaken via compressive sensing. To ensure the robustness and security of our algorithm and the convenience of subsequent embedding operations, each block is merged, quantized, and disturbed again to obtain the secret image. In particular, landscape paintings have a characteristic hazy beauty, and secret images can be camouflaged in them to some extent. For this reason, in this paper, a landscape painting is selected as the carrier image. After a 2-level discrete wavelet transform (DWT) of the carrier image, the low-frequency and high-frequency coefficients obtained are further subjected to a discrete cosine transform (DCT). The DCT is simultaneously applied to the secret image as well to split it. Next, it is embedded into the DCT coefficients of the low-frequency and high-frequency components, respectively. Finally, the encrypted image is obtained. The experimental results show that, under the same compression ratio, the proposed image compression-encryption algorithm has better reconstruction effect, stronger security and imperceptibility, lower computational complexity, shorter time consumption, and lesser storage space requirements than the existing ones.

In this article, we make a comparative study for a new approach compression between discrete cosine transform (DCT) and discrete wavelet transform (DWT). We seek the transform proper to vector quantization to compress the EMG signals. To do this, we initially associated vector quantization and DCT, then vector quantization and DWT. The coding phase is made by the SPIHT coding (set partitioning in hierarchical trees coding) associated with the arithmetic coding. The method is demonstrated and evaluated on actual EMG data. Objective performance evaluations metrics are presented: compression factor, percentage root mean square difference and signal to noise ratio. The results show that method based on the DWT is more efficient than the method based on the DCT.

The most vivacious area of the image processing is image enhancement. Newer techniques and ideas are being routinely incorporated to this field for the proper enhancement to make the original image suitable for some specific purposes. However, the techniques that are suitable for X-ray image enhancement may not necessarily be suitable for enhancement of the Satellite Telescope Transmitted (STT) images. Many times, Medical images especially X-ray images are required to be sharper than its original version for proper information extraction that is necessary for diagnostic purposes. Homomorphic filters that actually belong to the group of the sharpening filters can be employed for finding fine details in the X-ray images. The Homomorphic filters use the Discrete Fourier Transforms (DFT) as the core transform. Presently, more efficient tools for transformations are being used; such as the Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), Fast Fourier Transform (FFT) and Fast Wavelet Transform (FWT) in digital image processing. In this paper, along with the conventional DFT technique, DCT, DWT, FFT and FWT are incorporated in the image transformation process that consequently modifies the core process of Homomorphic filters. The performance of the resulting modified Homomorphic filters are compared with that of the original filter. The performance enrichment has become evident from the numerical and the visual comparisons.

The success of internet technology transform the world of technology and fashioned our life such a lot easier. The matter of duplication and unauthorized use of information become a great threat within the field of technology. To beat these problems, techniques like digital watermarking, steganography and cryptography were introduced. The approach of embedding a secret data associated with the digital signal inside the signal itself is digital watermarking. For embedding and detecting the watermark different techniques are used; spatial domain techniques like Least Significant Bit (LSB) and Patch Work Algorithm, then the frequency domain techniques such as Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) and Discrete Fourier Transform (DFT) are some of them. Combination of DCT & DWT technique for digital watermarking is proposed here. The proposed methodology is implemented in MATLAB 2017a simulator and result is analysed using evaluation parameters like Peak Signal to Noise Ratio (PSNR) & Mean Square Error (MSE). PSNR value obtained for the case of watermarking using DWT is 27.46 and MSE value is 17.45. The value of PSNR for watermarking using DCT is 41.4 and for MSE the value is 0.67. The PSNR and MSE values obtained for watermarking using LSB technique is 50.55 and 0.58. The proposed method improves the watermarked image quality and the MSE & PSNR value obtained is 0.52 and 51.017 respectively.

Compressed sensing (CS) algorithms exploit sparseness properties to reconstruct high spatial resolution magnetic resonance (MR) images from k-space data acquisitions significantly under sampled to reduce imaging times. CS algorithm effectiveness is frequently shown using under-sampled k-space data from NxN simulated images. These demonstration reconstructions are near perfect with quality higher than reconstructions using under-sampled NxN experimental k-space data sets. These differences are explained in terms of the interaction between the explicit transform domain sparsity requirement employed during iterative CS reconstruction and an inherent frequency domain property of the discrete Fourier transform (DFT). We report on experiments to overcome the limitations imposed by this DFT property by modifying the CS objective function to use a sparseness transform with a resolution higher that the standard transform related to the acquired NxN data matrix size. We demonstrate the relative effectiveness and limitations of standard CS and our proposed highresolution k-space extrapolation enabled (Hi-KEE) CS reconstruction on underand fully-sampled, simulated and experimental MR k-space data. (8 pages)

Microwave Imaging offers safe, low-cost, and portable method for medical imaging applications. These advantages make the microwave imaging convenient for early detection of tumor or cancer. The transmission method is one of the methods in microwave imaging which provides fast measurement and simple image reconstruction. However, this method requires a great number of measurements to obtain a well-reconstructed image. In order to reduce the number of measurements, this research proposes a Compressive Sensing (CS) approach for image reconstruction on microwave imaging. Compressive Sensing allows reconstruction of a signal with fewer measurements than the conventional approach. In this research, the scanning process is conducted on Computer Simulation Technology (CST) Microwave Studio software. Two dipole antennas with 3 GHz frequency are utilized as microwave transmitter and receiver. A two-layer cube phantom acts as the scanned object. Each layer has different relative permittivity which illustrates the healthy cell and abnormal cell. To meet the framework of Compressive Sensing, a weighted matrix of Discrete Radon Transform (DRT) is created as a projection matrix which delineates the data acquisition scheme in the scanning process. Discrete Cosine Transform (DCT) is selected as sparse dictionary matrix to represent the sparse basis while Basis Pursuit is selected as sparse reconstruction algorithm to reconstruct the sparse signal from measurement data. The measured $S_{21}$ data are successfully reconstructed into an image using the Compressive Sensing approach. The reconstructed image is analyzed both qualitatively and quantitatively using image quality parameters such as Structural Similarity Index (SSIM) and Mean Squared Error (MSE).

Presents two novel algorithms for compression of multilead electrocardiograms (MLECGs). In the first, the MLECG was decorrelated using a discrete cosine transform (DCT) and then a discrete wavelet transform (DWT) was applied on each channel after the removal of the least significant channels in the DCT domain. Significant compression ratios (CR) were achieved by retaining only the consequential DWT coefficients. The full potential of DWT was further exploited by appropriate quantization of these coefficients. Near perfect reconstruction was obtained for a CR of 1:8. This approach is highly suited for real time applications including that of high frequency Holter ECG. In the other algorithm, first level of compression was achieved by truncating the DWT while storing the highly significant coefficients from the truncated portion. Transform domain pole-zero modeling (TDPM) was then applied on the DWT compressed ECG to achieve higher compression ratios. In TDPM the DCT of a cycle of ECG is modeled as the impulse response of a pole-zero filter using Smith's (1983) method. Further compression was achieved by the application of vector quantization (VQ) on the model parameters. This algorithm resulted in a CR of 1:80 without significant distortion. The accuracy of reconstruction was checked using both qualitative and quantitative measures. The proposed algorithms were validated on both standard and local databases.