An Approximate Adder With a Near-Normal Error Distribution: Design, Error Analysis and Practical Application

Adders play a critical role as primary modules in circuit design, supporting error-tolerant applications such as machine learning, digital image processing, and signal processing. Therefore, the development of adders with low power consumption and energy efficiency is of utmost importance. Approximate adders outperform exact adders in VLSI chips. Among approximate adders, the hybridization of Single Exact and Single Approximation (SESA) and Single Exact and Dual Approximation (SEDA) techniques has emerged as a promising solution. These hybrid adders offer superior power and energy savings relative to other accurate and approximate adder designs. In this scheme, we propose the integration of hybrid radix-4 adders with approximation adders to achieve enhanced performance and pave the way for future hybrid approximate adder circuits. Extensive simulations validated the efficacy of the proposed approach. Furthermore, practical applications demonstrated the versatility and potential of hybrid adders in real-world scenarios. The proposed methodology ensures cost-effectiveness and facilitates seamless future updates and extensions. Overall, this research contributes to the advancement of efficient and low-power adder designs, addressing the evolving requirements of modern digital systems.

Objectives: Image Denoising refers to the recovery of an image that has been corrupted by noise due to poor quality of image acquisition and transmission. Accordingly, there is a need to reduce the noise present in the image as a consequence of the denoised image formed. Methods/Statistical Analysis: This paper presents Image denoising using Wavelet transforms, Contourlet transforms and Block Matching Transforms governed by bivariate shrinkage (Bi-shrink) filter techniques. The Wavelet transform uses up-sampling, down-sampling, low pass filter and high pass filter to perform denoising operation, the Contourlet transform uses up-sampling, down-sampling, low pass filter and high pass filter and directional filter banks to perform denoising operation, the Block Matching Transform uses Haar Transforms, Discrete cosine transforms and Karhunen Loeve transform to perform denoising operation. Findings: The performance of wavelet transforms, Contourlet transforms and Block Matching Transforms are evaluated for Reference images (such as towers, shades and ruler images) corrupted by gaussian noise and salt and pepper noise, by computing two error metrics Peak Signal to Noise Ratio (PSNR) and Execution Time (ET) with help of shrinkage function. Programming these using MATLAB R2014a by exploring its wavelet transform, Contourlet transform, image processing and signal processing toolboxes and the values are presented in tabular forms and discussed in the section 6. In this paper the block matching haar discrete cosine transform is proposed for denoising of images (especially for those images possessing detailed textures) that works through haar transform and discrete cosine transform outstrips the basic transform discrete wavelet transform and semi translation invariant contourlet transform. For the images corrupted by Gaussian noise and denoised by the proposed transform outstrips the basic transform “Discrete Wavelet Transform by PSNR = 6.71 dB, ET = 25.89 sec” and “Semi Translation Invariant Contourlet Transforms by PSNR = 5.49 dB, ET = 5.89 sec”. For the images corrupted by Salt and Pepper noise and denoised by the proposed transform outstrips the basic transform “Discrete Wavelet Transform by PSNR = 21.15 dB, ET = 0.27 sec” and “Semi Translation Invariant Contourlet Transforms by PSNR = 20.05 dB, ET = 5.80 sec”. Application/Improvements: In this paper Block Matching Haar Discrete cosine transform is proposed to overcome the limitations of wavelet transforms and Contourlet transforms, hence to attain the trade-off between high peak signal to noise ratio and less execution time. Results and Discussion section illustrates the efficacy of the proposed transform in terms of peak signal to noise ratio, execution time and visual quality of images.

With the growth of big data applications such as voice/speech recognition, data mining, and computer vision, conventional computing system faces significant challenges. The increasing computational complexity and large data set results in large power consumption. To address this challenge, we propose to combine the benefits of approximate and in-memory computing which effectively reduces power consumption without any significant impact on the output. In this work, a low power approximate adder based on nonvolatile memory element (Magnetic Tunnel Junction (MTJ)) is designed for a wide range of applications. Furthermore, the proposed approximate adder is demonstrated to perform edge detection on a 512x512 image using the Sobel Edge Detection Algorithm. The effect on the quality of image using metrics like mean square error (MSE), peak signal to noise ratio (PSNR), and structural similarity index (SSIM) are also investigated.

Approximate computing is attracting attention as an energy-efficient design, especially suitable for Deep Neural Network and Image Processing. In this study, a variety of approximate adders are applied to a hardware accelerator of 8 by 8 Matrix Multiplication in parallel structure to compare Error Distance and Error Rate. In the simulations, each shows different error figures according to metrics for the reliability, and AMA1, InXA2 and VAXA show the fewest errors according to the indicators. In addition, it shows that various approximate adders have few errors that can be used for matrix multiplication, and that parallel structures and approximate computing can be used appropriately for matrix operations.

Digital image processing is versatile research in this era. Many researchers implement different types of organizations like image restoration, image enhancement, color image processing, image segmentation etc. Image enhancement technique is among the simplest and most appealing area of digital image processing. Enhancement techniques like brightness preservation, contrast enhancement highlight certain features means depend which part of the image want to be enhance some application some input image including noise, reduction or removal of noise is also form of image enhancement. Brightness preservation has enhanced visual quality of digital image so that the limitation contained in these images is used for various applications in a better way. A very popular technique for image enhancement is histogram equalization (HE) and curvelet transformation. HE technique is commonly employed for image enhancement because of its simplicity and comparatively better performance on almost all types of images. Another widely used technique is curvelet transformation. This technique is identified and separate bright regions of image but more error rate and low peak signal to noise ratio(PSNR), result of this technique is brightness preservation level is low and output image is gray. This paper design a hybrid model through discrete cosine transformation, discrete wavelet transformation and combine output of both techniques with image fusion. Proposed algorithm enhanced features and removal noise by decomposition of image using DWT and discrete cosine transformation, adaptive histogram equalization is very important part in this algorithm for smooth image. The tested results of different images are comparing with previous method, generating result with different parameters; less mean square error and high PSNR for improve the quality of an image. This paper presents a hybrid model used various parameter for enhance images like satellite images, medical images etc.

In this study, dimensions, mass and shape characteristics of five commercial loquat cultivars (‘Akko XIII’, ‘Champagne de Grasse’, ‘Guzelyurt 6’, ‘Hafifcukurgobek’ and ‘Sayda’) and two genotypes (‘KKTC3’ and ‘KKTC4’) were determined. Physical properties such as dimension and shape were determined both by digital caliper and image processing to compare each other. Among the cultivars and genotypes tested, ‘KKTC4’ (58.88 mm) had the highest length while ‘KKTC3’ had the highest major diameter, minor diameter, mass, geometric mean diameter, surface area and volume, with a mean of 46.31 mm, 43.61 mm, 60.12 g, 48.69 mm, 74.82 cm2, and 61.25 cm3, respectively. The greatest value of elongation and the smallest value of sphericity were obtained from ‘Akko XII’ with 1.33, and ‘Akko XII’ was more oblong than the other cultivars and genotypes. The smallest value of elongation and the greatest value of sphericity were obtained from ‘Sayda’ with 1.12 and 91.16%, respectively. The results of comparison between the digital caliper and image processing showed that using the image processing method could potentially be rapid and alternative to the conventional measurement method. Key words: Eriobotrya japonica, image processing, loquat, physical properties.

To reduce power consumption, approximate computing is an efficient approach for error-tolerant applications such as image processing. Approximate arithmetic adders can be used for the approximate computing, and can trade off accuracy for power. CMA, a dynamically accuracy-configurable approximate adder, had been proposed. CMA can sharply reduce power consumption compared with other accuracy-configurable approximate adders, while allowing it to change accuracy-setting at run-time. In this paper, we propose a tiny error corrector for CMA that needs to only two gates for each digit. By consuming 1.4% extra power, the proposed value corrector can improve accuracy for CMA by up to 29.3% on average.

Full-scale aircraft structural fatigue testing exposes structural weaknesses by simulating the use of the aircraft in service and monitoring the development and expansion of fatigue cracks to guide the optimisation of aircraft structural design, the determination of service life and the development of maintenance and repair programmes. If crack damage is not detected in time, the uncontrolled expansion of the crack may lead to structural damage and prolong the test cycle. Therefore, it is crucial to achieve accurate detection of early cracks in fatigue testing of aircraft structures. Digital image technology is a new technology supported by a number of technical and theoretical achievements. In practical application, it relies on the support of computer functions, by converting image information into two-dimensional digital signals, thus realising various operations. In this paper, digital image processing techniques are used to deepen the backbone feature extraction network structure and improve the prediction scale of small targets, thus improving the performance of the model in terms of feature extraction and small defect detection. Experimental results show that the method can achieve accurate detection of small cracks, providing an effective technical approach for the automatic detection of cracks in aircraft structural fatigue tests. The technique of detecting cracks in aircraft structures using digital image processing also provides a new idea for research into improving aircraft endurance testing, which can be further developed with the aid of image technology.

Digital radiography systems are capable of capturing a wide range of x‐ray exposures in a single image. The wide latitude of these capture devices dictates that images are digitally processed before display. Attempting to directly print or display the full dynamic range of the captured image will result in an image with low contrast that is unacceptable for diagnostic interpretation. Image processing algorithms are used to identify the range of exposures (represented as code values) that correspond to the diagnostically relevant regions, followed by a rendering process to transform signal values in the diagnostically relevant regions to display values. The image processing algorithms need to perform these steps completely automatically, or with a minimum amount of human intervention, to facilitate technologists' workflow. Image processing performance is ultimately gauged by the ability to automatically and consistently generate images of diagnostic quality. Recognition of the diagnostically relevant exposures consists of segmentation of the collimation, direct exposure, and anatomy regions. This is a challenging computer‐recognition problem because several factors cause the characteristics of the image, and corresponding code value histogram, to vary. These factors include the body part and projection, exposure technique, collimation, use of anti‐scatter devices, use of contrast media, etc. Robust segmentation will also automatically recognize other features such as prosthetic implants, pacemakers, and left‐right markers. Once the image is properly segmented, the signal values for the diagnostically relevant regions are transformed into values for display. Rendering the region of interest for display generally consists of establishing the image grayscale rendition, and signal equalization and contrast enhancement, which is based on spatial frequency decomposition and reconstruction. Because of the tremendous flexibility to render images to different aims, understanding the rendering preferences of radiologists is a critical component of digital radiography image processing. Establishing the aim appearance for different exam types, then adapting the image processing algorithms and database parameters to automatically and consistently deliver the preferred rendering, will affect both the technologists' and the radiologists' satisfaction with the capture device. This course will review fundamentals of image processing for digital radiography. Specific course content will include a discussion of radiographic image segmentation, correlation of image content with different regions of the histogram, and a review of image‐rendering functions, including the tone scale, spatial frequency methods to enhance contrast, and signal equalization. The course will also include a review of the role of image processing in the end‐to‐end image chain (capture through interpretation), with considerations for image quality performance of different capture and display devices, the effect of the human visual system and ambient viewing conditions, and grayscale calibration.

The Quadric Error Metric (QEM) [1] criterion has been widely applied in mesh simplification procedures. Related criteria--such as the Quasi-Covariance Error Metric (QCEM) [2], which may produce superior results to the QEM--have also been reported in recent years. In this paper, the underlying reasons that criteria such as QEM and QCEM are so successful in mesh simplification processes are considered through analysis of error in the simplification process. Focus is on the use of the QEM and QCEM criteria in edge contraction-based mesh simplification.

Introduction: Approximate computing is one of the techniques used to balance trade-offs between power, speed, and area in a resource-limited environment. Mainly, a large amount of power consumption and significant delay are caused by the arithmetic operations, in which the multiplication process generates more power consumption and high latency. In order to save energy and increase speed, an approximate multiplier is a good candidate for use in error-resilient applications like signal and image processing. This study proposes a truncated adaptive approximate radix-8 Booth multiplier (TAARBM). It aims to apply partial product truncation to construct an approximation multiplier design for error-tolerant applications, such as image processing. Methods: The truncation strategy is adopted to minimize the partial product array (PPA) of the radix- 8 Booth multiplier, as an additional PPA creates complexity in the operations. Moreover, the Booth encoder in the radix-8 Booth multiplier is enhanced with an Approximate Booth Encoder (ABE), which replaces adders with simple shift-logic operations to speed up the operation. The path Selectable and Reconfigurable Hybrid Adder (pSRHA) is introduced in the TAARBM architecture to minimize the delay. The design is coded in Verilog-HDL, simulated on the Xilinx Vivado simulator, and implemented on an FPGA board. Results: The simulation results demonstrate that the proposed 16-bit TAARBM consumes 4.110 W power and 1.805 ns delay. The proposed design accomplishes error metrics of 402.96 MED, 0.00975 MRED, 1300 AED, and 0.0120 ARE. Discussion: The simulation results show the proposed design';s high-speed operation. Moreover, the proposed approximate multiplier is designed with a low error rate, as shown by performing different error metrics like MED, MRED, AED, and ARE. In addition, the FIR filter is designed with the proposed TAARBM to perform the image denoising process on five benchmark images. For this application, the image quality measures, such as PSNR and SSIM, are calculated, which are higher for the proposed design. Conclusion: The comparison of the obtained results with existing references proves the present validity of the current work. Various error metrics and synthesis results validate the effectiveness of the proposed approximate multiplier. Moreover, the proposed multiplier is used in an image processing application for the denoising process.

Introduction Peripheral arterial disease (PAD) is a fairly common degenerative vascular condition in diabetic patients that leads to inadequate blood flow (BF), this disease is mainly due to atherosclerosis that causes chronic narrowing of arteries, which can precipitate acute thrombotic events. In patients with diabetes, atherosclerosis is the main reason for reducing life expectancy, as long as diabetic nephropathy and retinopathy are the largest contributors to end-stage renal disease and blindness, respectively. Objective This was an assessment of dilatation of the blood vessels on diabetic patients vs. healthy volunteers by using digital processing of imaging’s. Materials and Methods The study subject was ultrasound imaging processing of blood vessels dilation on low extremities of diabetic patients, the results were compared with ultrasound images of healthy subjects. Results The digital images processing suggests that there is a significant difference among images experimental of the diabetic group and healthy volunteers’ images, the control group. Discussion The digital imaging processing performed in the Matlab platform is an adequate procedure for blood vessels dilation analysis of the ultrasound images taken from the lower extremities in diabetic patients.

As modern computing systems face escalating demands for performance under strict power constraints, approximate computing has emerged as a critical design paradigm. This paper presents the design, implementation, and comprehensive analysis of a novel 32-bit hybrid accurate-approximate adder architecture. The proposed design strategically combines a Kogge-Stone Parallel Prefix Adder for the most significant part with a lowpower, structurally simple approximate Ripple-Carry Adder for the least significant part for case 1, and a sum-less adder for case 2. The design was implemented in a modular Verilog hierarchy and subjected to a rigorous analysis using Xilinx Vivado for various partition configurations (k). Our post-implementation results demonstrate significant hardware efficiency gains: the total power consumption is reduced by up to 29 % and LUT area is reduced by up to 74.3 % in case of a hybrid KSA+ approximate adder(case 1) and up to 91.4 % in area and up to 48.3 % in power for a KSA+ sum-less hybrid adder design (case 2) as the hybrid partition parameter, k, is increased. However, a detailed error analysis reveals that the high error rates, which saturate near 100 % for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k \geq 16$</tex> (case 1), are dominated by error from the approximate section. We also observed that even though overall error rates can saturate as the value of k is increased, the fact that the most significant bits remain accurate as k is increased allows one to leverage this behaviour for various applications where only the most significant bits of the final sum are important. This work thoroughly characterizes a unique design point in the power-performance-accuracy space, concluding that this architecture is highly effective for applications where hardware cost is the primary concern and error tolerance is high.

Approximate arithmetic circuits are designed to improve energy efficiency and performance in error-tolerant applications. The approximate arithmetic circuits behave differently for different applications. Also, the approximation may violate basic algebraic properties like commutativity, associativity, identity, etc. The violation of algebraic properties makes the output of the approximate circuits dependent on the order of the inputs. The existing work [1] has been on approximate adders and their application to image addition. This paper investigates the impact of approximation and commutativity in the 12 compressor-based multipliers for image processing applications and CNNs. The first observation is that the accuracy of the neural network drops drastically if the multiplication of zero is approximated. Second, the outcomes of neural networks and error-resilient image processing applications tend to differ depending on the order of the inputs. For instance, when the Yang2 [2] design is implemented on ResNet18, we observe an accuracy of 58.07% for \(a \times b\) and 69.4% for \(b \times a\). Based on our findings, we propose that prior knowledge can be used to organize input data to increase output quality for these applications.KeywordsError-resilienceApproximate computingCompressorsImage processing

In this study, a surface based strain measurement was used to determine the formability of the sheet metal. A strain measurement may employ manual calculation of plastic strains based on the reference circle and the deformed circle. The manual calculation method has a greater margin of error in the practical applications. In this paper, an attempt has been made to compare the formability by implementing three different theoretical approaches: Namely conventional method, least square method and digital based strain measurements. As the sheet metal was formed by a single point incremental process the etched circles get deformed into elliptical shapes approximately, image acquisition has been done before and after forming. The plastic strains of the deformed circle grids are calculated based on the nondeformed reference. The coordinates of the deformed circles are measured by various image processing steps. Finally the strains obtained from the deformed circle are used to plot the forming limit diagram. To evaluate the accuracy of the system, the conventional, least square and digital based method of prediction of the forming limit diagram was compared. Conventional method and least square method have marginal error when compared with digital based processing method. Measurement of strain based on image processing agrees well and can be used to improve the accuracy and to reduce the measurement error in prediction of forming limit diagram.