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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
The inverse transform is identical. The Hadamard transform was formerly used for data compression because its entries are all 1 or -1, allowing computation without multiplications. In this context it is now superseded by the discrete cosine transform. half adder a logic circuit that produces the sum and carry outputs for two input signals. A half adder has no carry input. half bridge amplifier a class-D amplifier based on a half-bridge inverter configuration. Not suitable for amplification of DC to low-frequency signals because the capacitor leg cannot provide unidirectional current. half subtracter a logic circuit that provides the difference and borrow outputs for two input signals. A half subtracter has no borrow input. half-band filter a filter whose even-indexed coefficients are all zeros except the one in the filter center. half-height point a point at which the membership grade is equal to 0.5.
Discrete 2-D Fourier Transform
Published in Artyom M. Grigoryan, Merughan M. Grigoryan, Image Processing, 2018
Artyom M. Grigoryan, Merughan M. Grigoryan
The theory of the continuous-time and discrete-time Fourier transformations has been well developed. The discrete Fourier transform has become a powerful technique in signal processing, and in particular in image processing. Effective methods, or fast algorithms, [1]–[6], of the discrete Fourier transforms (DFT) are used for solving many problems in image processing in the frequency domain, such as image filtration, restoration, enhancement, compression, and image reconstruction by projections [7]–[10]. Other unitary transformations are also used in signal and image processing. Considerable interest is given to many applications of the discrete Hartley transformation (DHT), since it relates closely to the DFT and has been created as an alternative form of the complex DFT to eliminate the necessity of using complex operations [11]–[15]. The discrete cosine transformation (DCT) is used in speech and image processing, especially in image compression and transform coding in telecommunication [16]–[22]. Another unitary transformation is the discrete Hadamard transformation (DHdT), whose basic functions take value ±1 at each point [23]–[48]. The Hadamard transform has found useful applications in signal and image processing, communication systems, image coding, image enhancement, pattern recognition, and general two-dimensional filtering [2, 7].
Discrete Signal Transformations
Published in Leonid P. Yaroslavsky, THEORETICAL FOUNDATIONS of DIGITAL IMAGING Using MATLAB®, 2012
can also be computed using fast Hadamard transform algorithm, though it must be complemented with permutation of transform coefficients according to their gray code ordering. Similarly to Hadamard transform, inverse Walsh transform is identical to the direct one.
Optimal blind colour image watermarking based on adaptive chaotic grasshopper optimization algorithm
Published in The Imaging Science Journal, 2022
Digital watermarking methods fall into two general classifications, namely Spatial and Frequency Domain Watermarking. In the spatial watermarking domain, the pixel values of the host image are changed directly to embed watermark. The frequency domain method embeds the watermark in the transformed coefficients of the host image. The recently used transforms are Fourier Transform [6], Hadamard Transform [7], Discrete Cosine Transform (DCT) [8], Lifting Wavelet Transform (LWT) [9], Discrete Wavelet Transform (DWT) [10], Walsh Hadamard Transform [11] and Hybrid Transform [12–14]. LWT is an efficient wavelet of the second generation which is also known as the Lifting Scheme. This frequency domain watermarking method [15] is preferrable than the spatial domain watermarking because it reveals strong transparency and robustness.
Electroencephalography applied compression algorithms qualitative analysis
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2020
Aratã Andrade Saraiva, Felipe Miranda de Jesus Castro, Renato Conceição Nascimento, Rodrigo Teixeira de Melo, José Vigno Moura Sousa, Antonio Valente, Nuno Miguel Fonseca Ferreira
They are very useful in reducing the requirements of storage, bandwidth and spectrum analysis. Like Fast Fourier Transform (FFT) the WHT has a faster version to Fast Walsh Hadamard Transform (FWHT), which compared to FFT requires less storage space and is faster to calculate, since it uses only real additions and subtractions, whereas the FFT uses complex values.
Multimodal medical image fusion using residual network 50 in non subsampled contourlet transform
Published in The Imaging Science Journal, 2023
K. Koteswara Rao, K. Veera Swamy
The process whereby the collection of predominant information from registered multiple images to produce a distinct image is image fusion (IF). IF is one of the subfields of medical fields [1]. For the last few years, image fusion is identified as an important area in medical diagnosis because it gives complementary information with no loss of useful details in the input images. The result of the fusion is highly informative compared to the source images. Spatial and spectral resolutions are two considerable factors in image processing. The role of medical imaging is considered a high priority in clinical applications. Under discrepancy in the structure, images of various medical modalities target specific organ evolution. Medical images of different modalities give less amount of information. Computed tomography (CT) identifies the bony structure but it does not give delicate tissue information. Magnetic resonance imaging (MRI) gives higher information about delicate tissues but is unable to give dense structure information. The existing Positron emission tomography (PET) technique explores the statistics of the bloodstream in the organs but not the statistics of bones and delicate tissues. Similarly, the baseline Single photon emission computed tomography (SPECT) approach is good at metabolic information but cannot give useful details of bones and delicate tumours. The resolution of PET as well as SPECT is low compared to CT and MRI. Every modality has its own merits and drawbacks. Generally, physicians and radiologists analyze medical images of different modalities to get predominant information. Medical image fusion (MIF) is an adequate solution for this complication [2]. Individual modalities are not able to give such valuable information. Many fusion techniques have been introduced for several years [3–8]. The applications of IF are medical, remote sensing [8], military, and machine vision. There are two domains where image fusion is performed. One is spatial and another is the transform domain. Spatial methods are meant to consideration of pixel values directly. Averaging, IHS, brovey method, and PCA come into this category. In transform methods, a suitable transform is employed on the source images. It leads to the decomposition of frequency subbands. Different fusion rules are performed on these subbands and an inverse operation is performed to get the final fused output. Various well-known transforms are curvelet transform, contourlet transform, Discrete Sine Transform (DST), Rice Wavelet Toolbox (RWT), Discrete Fourier Transform (DFT), Discrete Hadamard Transform (DHT), Discrete Wavelet Transform (DWT), Discrete Cosine Transform (DCT), NSCT, NSST, and Singular Value Decomposition. Transform-based methods are most suitable for MIF. The fusion result depends on either selecting the optimal transform or selecting the optimal fusion strategy. Many fusion frameworks are based on the Multi-Scale Transform (MST). In MST-related approaches, the key entity images are decayed and these decomposition results are merged with the help of various fusion frameworks. The original image is attained by taking inverse transformation.