Error Diffusion Research Articles

High-quality and high-speed computer-generated holography via deep-learning-assisted bidirectional error diffusion method

Computer-generated holography (CGH) is an effective light field manipulation technique based on diffractive optics. Deep learning provides a promising way to break the trade-off between quality and speed in the phase-only hologram (POH) generation process. In this paper, a neural network called BERDNet is proposed for high-quality and high-speed POH generation. A high-quality POH dataset without speckle noise and shifting noise is generated by the band-limited bidirectional error diffusion (BERD) algorithm. Based on the dataset, BERDNet is trained to learn the potential hologram coding method for real-time POH prediction. Furthermore, the training process is constrained by both data loss and physical loss, so it is necessary to explore higher-fidelity reconstructions that are more consistent with the bandwidth limitation. Finally, the POHs of numerical reconstructions with an average of 23.13 dB PSNR can be obtained in 0.037 s, achieving 1-2 orders of magnitude acceleration. Experimental reconstructions validated the generalization of the BERDNet.

Over 100-fold improvement in the accuracy of relaxed eddy accumulation flux estimates through error diffusion

Measurements of atmosphere-surface exchange are largely limited by the availability of fast-response gas analyzers; this limitation hampers our understanding of the role of terrestrial ecosystems in atmospheric chemistry and global change. Current micrometeorological methods, compatible with slow-response gas analyzers, are difficult to implement, or rely on empirical parameters that introduce large systematic errors.Here, we develop a new micrometeorological method, optimized for slow-response gas analyzers, that directly measures exchange rates of different atmospheric constituents, with minimal requirements. The new method requires only the sampling of air at a constant rate and directing it into one of two reservoirs, depending on the direction of the vertical wind velocity. An integral component of the new technique is an error diffusion algorithm that minimizes the biases in the measured fluxes and achieves direct flux estimates.We demonstrate that the new method provides an unbiased estimate of the flux, with accuracy within 0.1% of the reference eddy covariance flux, and importantly, allows for significant enhancements in the signal-to-noise ratio of measured scalars without compromising accuracy. Our new method provides a simple and reliable way to address complex environmental questions and offers a promising avenue for advancing our understanding of ecological systems and atmospheric chemistry.

Fast view-specific generation of high-definition holograms with enhanced quality

Holography is often considered as the most promising immersive technology because it provides all the depth cues of the human visual system. Some limitations still need to be overcome such as the huge computational load of high-definition holograms and the noise introduced in the reconstructed scene during the quantization process. In this paper, we propose what we believe is a novel view-specific layer-based stereogram approach combined with a view-dependent error diffusion algorithm that aims to solve those limitations. This method selects the light waves of the 3D scene that reach a specific viewing area and leverages this particular configuration to apply an error diffusion algorithm. Two additional quality enhancement features are observed: the reduction of the conjugate order perceptibility and the increased brightness of the reconstructed scene. Numerical and optical experiments demonstrate the time savings and quality enhancements of our approach.

Binary image embedding and restoration in speech signal

AbstractIn this paper, we propose a method of embedding images into a speech signal. An image is embedded in the high frequency band above 16 kHz of the speech signal to be difficult to perceive for humans. In the proposed method, the image is embedded after being binarized by the error diffusion method. When the image is embedded, we apply an iterative phase restoration method to avoid noise generation. We also investigate a compensation method for an extracted image whose quality degrades due to transmission channel characteristics. Simulation and real‐environmental experiments showed that the proposed method significantly improved the quality of the extracted image on the receiver side.

A study on secured encryption of medical images using significant visual cryptography

The medical images of people are important and sensitive and cannot be shared with the public considering privacy measures. Maintaining the confidentiality of the medical image is essential, and leakage of such information can cause great loss. Therefore, the information has to be secured while being transferred through a third party, which can be any network medium. Thus, there is a need for developing a robust encryption algorithm. These algorithms improve the security of the ongoing pictures by compromising the nature of the picture and utilizing complex calculations. Algorithms that work on the nature of the picture by utilizing complex cycles, for example, error diffusion, halftoning, wavelet transform, and dithering, lead to time complexity. Thus, a compact and efficient cryptographic algorithm is proposed with fewer mathematical computations that ensure the secured transmission and reception of medical images through the medium using Significant Visual Cryptography (SVC). In SVC, initially, the quality of the secret images (SI) is improved by using the Error Abatement Technique (EAT). The output of EAT is used to generate random share values, which are then implanted in cover pictures. The shares that are transmitted do not reveal the secret information present in the original image because of the steganography features involved in this technique. The integrated check value (ICV) is calculated over the region of interest (ROI) at the encryption and decryption sides to provide additional security. Quality and security analyses have been carried out to ensure the robustness of the algorithm. The detailed study proved that the proposed algorithm beat the constraints of the current calculations. The concept of checking the integrity value and steganography features enhanced the effectiveness of the algorithm.

Efficient and Low-Complex Signal Detection with Iterative Feedback in Wireless MIMO-OFDM Systems.

To solve error propagation and exorbitant computational complexity of signal detection in wireless multiple-input multiple-output-orthogonal frequency division multiplexing (MIMO-OFDM) systems, a low-complex and efficient signal detection with iterative feedback is proposed via a constellation point feedback optimization of minimum mean square error-ordered successive interference cancellation (MMSE-OSIC) to approach the optimal detection. The candidate vectors are formed by selecting the candidate constellation points. Additionally, the vector most approaching received signals is chosen by the maximum likelihood (ML) criterion in formed candidate vectors to reduce the error propagation by previous erroneous decision, thus improving the detection performance. Under a large number of matrix inversion operations in the above iterative MMSE process, effective and fast signal detection is hard to be achieved. Then, a symmetric successive relaxation iterative algorithm is proposed to avoid the complex matrix inversion calculation process. The relaxation factor and initial iteration value are reasonably configured with low computational complexity to achieve good detection close to that of the MMSE with fewer iterations. Simultaneously, the error diffusion and complexity accumulation caused by the successive detection of the subsequent OSIC scheme are also improved. In addition, a method via a parallel coarse and fine detection deals with several layers to both reduce iterations and improve performance. Therefore, the proposed scheme significantly promotes the MIMO-OFDM performance and thus plays an irreplaceable role in the future sixth generation (6G) mobile communications and wireless sensor networks, and so on.

Defect detection of glassivation passivation parts wafer surface with random texture and different brightness

Automatic defect detection for glassivation passivation parts (GPP) wafer surface becomes an extremely challenging task, due to the interference of random texture, disturbance of low-contrast pseudo defects within the image, and difference of different brightness between images. In this paper, we propose a novel defect detection scheme for GPP wafer surface with random texture and different brightness. First, an automatic segmentation method center expansion idea-based for the region of interest (ROI) of die image is presented to eliminate the interference from edge background and improve the efficiency of defect detection. Then, a feature point set extraction method based on adaptive gain and error diffusion is proposed so that the defect feature between images with different brightness can be highlighted by adaptive gain, and the candidate defect feature point set under random texture feature is able to be extracted by error diffusion. Finally, the density-based spatial clustering of applications with noise considering grayscale constraint (GC-DBSCAN) is designed to identify the true defect clusters from the candidate defect feature point set and accomplish the detection of various types of surface defects. Experimental results show that the proposed method can completely implement the extraction of crack and dirty defects and eliminate the false detection caused by random texture and different brightness, which is very efficient and superior to other methods.

Comparison of double-phase hologram and binary amplitude encoding: holographic projection andvortex beam generation.

Utilizing computer-generated holograms is a promising technique because these holograms can theoretically generate arbitrary waves with high light efficiency. In phase-only spatial light modulators, encoding complex amplitudes into phase-only holograms is a significant issue, and double-phase holograms have been a popular encoding technique. However, they reduce the light efficiency. In this study, our complex amplitude encoding, called binary amplitude encoding (BAE), and conventional methods including double-phase hologram, iterative algorithm, and error diffusion methods were compared in terms of the fidelity of reproduced light waves and light efficiency, considering the applications of lensless zoomable holographic projection and vortex beam generation. This study also proposes a noise reduction method for BAE holograms that is effective when the holograms have different aspect ratios. BAE is a non-iterative method, which allows holograms to be obtained more than 2 orders of magnitude faster than iterative holograms; BAE has about 3 times higher light efficiency with comparable image quality compared to double-phase holograms.

Image Size-Preserving Visual Cryptography by Error Diffusion

Image Size-Preserving Visual Cryptography by Error Diffusion

Optical multiple-image authentication method based on Fourier single-pixel imaging and multiple logistic maps.

As a promising technique, the spatial information of an object can be acquired by employing active illumination of sinusoidal patterns in the Fourier single-pixel imaging. However, the major challenge in this field is that a large number of illumination patterns should be generated to record measurements in order to avoid the loss of object details. In this paper, an optical multiple-image authentication method is proposed based on sparse sampling and multiple logistic maps. To improve the measurement efficiency, object images to be authenticated are randomly sampled based on the spatial frequency distribution with smaller size, and the Fourier sinusoid patterns generated for each frequency are converted into binarized illumination patterns using the Floyd-Steinberg error diffusion dithering algorithm. In the generation process of the ciphertext, two chaotic sequences are used to randomly select spatial frequency for each object image and scramble all measurements, respectively. Considering initial values and bifurcation parameters of logistic maps as secret keys, the security of the cryptosystem can be greatly enhanced. For the first time to our knowledge, how to authenticate the reconstructed object image is implemented using a significantly low number of measurements (i.e., at a very low sampling ratio less than 5% of Nyquist limit) in the Fourier single-pixel imaging. The experimental results as well as simulations illustrate the feasibility of the proposed multiple-image authentication mechanism, which can provide an effective alternative for the related research.

Temporal-spatial binary encoding method based on dynamic threshold optimization for 3D shape measurement.

The binary encoding method has been widely used for three-dimensional (3D) shape measurement due to the high-speed projection characteristics of its digital mirror device (DMD)-based projector. However, traditional binary encoding methods require a larger defocus to achieve a good sinusoidality, leading to a reduction in the measurement depth of field and signal-to-noise ratio (SNR) of captured images, which can adversely affect the accuracy of phase extraction, particularly high-frequency fringes for 3D reconstruction. This paper proposes a spatial-temporal binary encoding method based on dynamic threshold optimization for 3D shape measurement. The proposed method decomposes an 8-bit sinusoidal fringe pattern into multiple(K) binary patterns, which can be outlined into two steps: determining the dynamic threshold and then performing temporal-spatial error diffusion encoding. By using an integral imaging strategy, approximate sinusoidal patterns can be obtained under nearly focused projection, which can then be subjected to absolute phase unwrapping and 3D reconstruction. The experiments show that compared to the three comparative algorithms under the same experimental conditions, this proposed method improves the reconstruction error of measuring a plane and an object by at least 13.66% and 12.57% when K=2. The dynamic experimental result on the palm confirms that the proposed method can reliably reconstruct the 3D shape of the moving object.

An Optimal Shaped Sensor Array Derivation.

In Structural Health Monitoring (SHM) applications, the Direction of Arrival (DoA) estimation of Guided Waves (GW) on sensor arrays is often used as a fundamental means to locate Acoustic Sources (AS) generated by damages growth or undesired impacts in thin-wall structures (e.g., plates or shells). In this paper, we consider the problem of designing the arrangement and shape of piezo-sensors in planar clusters in order to optimize the DoA estimation performance in noise-affected measurements. We assume that: (i) the wave propagation velocity is unknown, (ii) the DoA is estimated via the time delays of wavefronts between sensors, and (iii) the maximum value of the time delays is limited. The optimality criterion is derived basing on the Theory of Measurements. The sensor array design is so that the DoA variance is minimized in an average sense by exploiting the Calculus of Variations. In this way, considering a three-sensor cluster and a monitored angles sector of 90°, the optimal time delays-DoA relations are derived. A suitable re-shaping procedure is used to impose such relations and, at the same time, to induce the same spatial filtering effect between sensors so that the sensor acquired signals are equal except for a time-shift. In order to achieve the last aim, the sensors shape is realized by exploiting a technique called Error Diffusion, which is able to emulate piezo-load functions with continuously modulated values. In this way, the Shaped Sensors Optimal Cluster (SS-OC) is derived. A numerical assessment via Green's functions simulations shows improved performance in DoA estimation by means of the SS-OC when compared to clusters realized with conventional piezo-disk transducers.

Optical analog-signal transmission system in a dynamic and complex scattering environment using binary encoding with a modified differential method.

High-fidelity optical transmission through dynamic scattering media is challenging, since transmission errors are induced due to dynamic scattering media. In this paper, a new scheme is proposed to realize high-fidelity free-space optical analog-signal transmission in dynamic and complex scattering environments using binary encoding with a modified differential method. Each pixel of an analog signal to be transmitted is first divided into two values, and each of them is encoded into a random matrix. Then, a modified error diffusion algorithm is utilized to transform the random matrix into a 2D binary array. Each pixel of the analog signal to be transmitted is eventually encoded into only two 2D binary arrays, and transmission errors and dynamic scaling factors induced by dynamic and complex scattering media can be temporally corrected. Dynamic smoke and non-line-of-sight (NLOS) are created as a dynamic and complex scattering environment to verify the proposed method. It is experimentally demonstrated that analog signals retrieved at the receiving end are always of high fidelity using the proposed method, when average path loss (APL) is less than 29.0 dB. Only the half number of measurements is used compared to that in conventional methods. The proposed method could open up a novel research perspective for high-fidelity free-space optical analog-signal transmission through dynamic and complex scattering media.

Half-Tone Visual Cryptography Scheme For RGB Color Images

Objectives: Currently used visual-cryptography methods which use binary and gray-level images have some shortcomings such as large pixel expansion, poor visual quality of the reconstructed image, etc. Further modifications in visualcryptography methods are required to provide error-free and better results. It has been observed that the use of color images is more convenient and accurate in approach. Method: This research study presents a new and optimal scheme for the visual-cryptography which is centered on RGB color images. Jarvis halftoning is applied on each decomposed color channel that is used in share generation. A special code matrix is defined for the generation of color shares and the optimal reconstruction of the original image. The method is tested with color images of different sizes, no specific dataset is required. Pixel Expansion, The Aspect Ratio, and Contrast of the method is compared with the existing method, and found more enhanced result. Findings: The scheme projected eliminates the problems of large pixel expansion and poor visual quality in the reconstructed images. The performance of the method is tested with the different statistical measures and values obtained as Mean Square Error (MSE):0, Peak- Signal-to-Noise-Ratio (PSNR): ¥, Universal Index Quality (UIQ):1, etc. This means that the original image is completely recovered with good contrast. Novelty: Color images of varied sizes and channels can be processed by applying the Jarvis half-toning technique through the codebook calculated to abolish the problems of pixel expansion and to improve the superiority of the renovated image. Keywords: Color HalfTone Images; Error Diffusion; Optimal Contrast; Secret and Secure Sharing Scheme; Expansion of Pixels

Descreening of dispersed-dot halftone images with generative adversarial network

Halftoning a continuous-tone image inherently results in loss of information, which makes the inverse process, descreening, a challenging problem. Current state-of-the-art descreening algorithms have two issues: first, they mostly are PSNR-oriented reconstruction algorithms, which tend to generate piecewise smooth images that do not appear realistic due to their lack of texture. Furthermore, these algorithms are typically trained with halftone images generated from the Floyd-Steinberg error diffusion algorithm, which is not an optimal choice since the algorithm is known to generate visible artifacts in the halftone image. We address these issues by the following: first, we propose a new descreening algorithm based on conditional generative adversarial networks (cGAN) that generate descreened images with abundant texture resulting in more realistic appearance. Next, we propose using the direct binary search (DBS) algorithm instead of Floyd-Steinberg error diffusion for generating the halftone images, since it is known to generate halftone images without visible artifacts. Both qualitative and quantitative comparisons show that our algorithm outperforms state-of-the-art descreening algorithms significantly.

Parallel Graph Signal Processing: Sampling and Reconstruction

Graph signal processing (GSP) extends classical signal processing methods to analyzing signals supported over irregular grids represented by graphs. Within the scope of GSP, sampling and reconstruction represent fundamental tools that have received considerable attention. For very large graphs, however, many of the current methods struggle with the computational and memory requirements. Vertex domain and randomized sampling strategies somewhat ameliorate the computational requirements, but these algorithms perform poorly at preserving signal fidelity for graphs with hundreds of thousands of vertices. To address these shortcomings, this paper introduces a new and scalable approach that can be easily parallelized. This new approach uses existing graph partitioning algorithms in concert with vertex-domain blue-noise sampling and reconstruction, performed independently across partitions. In the reconstruction, some degree of overlapping is added to the partitions to induce trans-partition smoothness in the recovered signal. We also propose two sampling schemes based on the spatial characteristic of the graph that minimizes the recovery error. The first combines graph partitioning with the Void-and-Cluster algorithm, while the second approach uses Error Diffusion. We conclude this paper with experiments on synthetic and real data that show the effectiveness of these new approaches on very large graphs.

Efficient Halftoning via Deep Reinforcement Learning.

Halftoning aims to reproduce a continuous-tone image with pixels whose intensities are constrained to two discrete levels. This technique has been deployed on every printer, and the majority of them adopt fast methods (e.g., ordered dithering, error diffusion) that fail to render structural details, which determine halftone's quality. Other prior methods of pursuing visual pleasure by searching for the optimal halftone solution, on the contrary, suffer from their high computational cost. In this paper, we propose a fast and structure-aware halftoning method via a data-driven approach. Specifically, we formulate halftoning as a reinforcement learning problem, in which each binary pixel's value is regarded as an action chosen by a virtual agent with a shared fully convolutional neural network (CNN) policy. In the offline phase, an effective gradient estimator is utilized to train the agents in producing high-quality halftones in one action step. Then, halftones can be generated online by one fast CNN inference. Besides, we propose a novel anisotropy suppressing loss function, which brings the desirable blue-noise property. Finally, we find that optimizing SSIM could result in holes in flat areas, which can be avoided by weighting the metric with the contone's contrast map. Experiments show that our framework can effectively train a light-weight CNN, which is 15x faster than previous structure-aware methods, to generate blue-noise halftones with satisfactory visual quality. We also present a prototype of deep multitoning to demonstrate the extensibility of our method.

Flexible Error Diffusion Algorithm for Binary Defocusing Fringe Projection Profilometry

The error diffusion algorithm shows great potential in binary defocusing fringe projection profilometry (FPP) for improving the intensity representation of binary patterns. However, the fixed kernel in the error diffusion algorithm makes the generated binary patterns far from optimal patterns because of ignoring the structural differences of patterns and the intensity error induced by the coupling effect among binary patterns. This article proposes a flexible error diffusion algorithm with an unfixed kernel to generate high-quality binary patterns for binary-defocusing FPP, thereby realizing rapid and accurate 3-D shape reconstruction. Dual-objective functions are adopted in the proposed approach for kernel optimization. First, taking the minimum intensity error as one objective, this work presents an unfixed four-coefficient error diffusion algorithm to generate binary patterns with the best intensity representation. Second, taking the minimum phase error as another objective, a dual-objective error diffusion algorithm is developed to select the binary patterns with the best phase quality in the phase domain. Finally, a local intensity correction (LIC) procedure eliminates phase jump errors in the encoding phase of the selected binary patterns to get the optimal projections for binary-defocusing FPP. Simulated and experimental results verify that the binary patterns generated using the proposed approach can support the accurate binary-defocusing FPP at various degrees of defocusing.

Full-resolution, full-field-of-view, and high-quality fast Fourier single-pixel imaging.

Fourier single-pixel imaging (FSI) uses Fourier basis patterns for spatial light modulation to acquire the Fourier spectrum of the object image. The object image can be reconstructed via an inverse Fourier transform. However, the Fourier basis patterns are inherently gray scale, which results in the difficulty that the patterns can hardly be generated at a high speed by using a commonly used spatial light modulator-digital micromirrors device. To tackle this problem, fast FSI, which uses upsampled and dithered Fourier basis patterns to approximate the gray scale patterns, has been reported, but the achievable spatial resolution has to be sacrificed in the pattern upsampling process. Here we propose a method that can achieve not only full-resolution but also full-field-of-view and high-quality FSI. The key to the proposed method is to use a new, to the best of our knowledge, error diffusion dithering algorithm combined with two different scanning strategies to generate two sets of binarized Fourier basis patterns for spatial light modulation. As a result, two images with a sub-pixel shift from each other are reconstructed. It results in the final high-quality reconstruction by synthesizing the two images. We experimentally demonstrate the method can produce a high-quality 1024 × 768-pixel and full resolution image with a digital micromirror device with 1024 × 768 micromirrors.

Lensless phase-only holographic retinal projection display based on the error diffusion algorithm.

Holographic retinal projection display (RPD) can project images directly onto the retina without any lens by encoding a convergent spherical wave phase with the target images. Conventional amplitude-type holographic RPD suffers from strong zero-order light and conjugate. In this paper, a lensless phase-only holographic RPD based on error diffusion algorithm is demonstrated. It is found that direct error diffusion of the complex Fresnel hologram leads to low image quality. Thus, a post-addition phase method is proposed based on angular spectrum diffraction. The spherical wave phase is multiplied after error diffusion process, and acts as an imaging lens. In this way, the error diffusion functions better due to reduced phase difference between adjacent pixels, and a virtual image with improved quality is produced. The viewpoint is easily deflected just by changing the post-added spherical phase. A full-color holographic RPD with adjustable eyebox is demonstrated experimentally with time-multiplexing technique.