Accurate Image Reconstruction Research Articles

Joint [Formula: see text] and Image Reconstruction in Low-Field MRI by Physics-Informed Deep-Learning.

We present a model-based image reconstruction approach based on unrolled neural networks which corrects for image distortion and noise in low-field ( B0 ∼ 50 mT) MRI. Utilising knowledge about the underlying physics, a novel network architecture (SH-Net) is introduced which involves the estimation of spherical harmonic coefficients to guarantee a spatially smooth field map estimate. The SH-Net is integrated in an end-to-end trainable model which jointly estimates the B0-field map as well as the image. Experiments were conducted on retrospectively simulated low-field data of human knees. We compare our model to different model-based approaches at distinct noise levels and various B0-field distributions. Our results show that our physics-informed neural network approach outperforms the purely model-based methods by improving the PSNR up to 11.7% and the RMSE up to 86.3%. Our end-to-end trained model-based approach outperforms existing methods in reconstructing image and B0-field maps in the low-field regime. low-field MRI is becoming increasingly more popular as it enables access to MR in challenging situations such as intensive care units or resource poor areas. Our method allows for fast and accurate image reconstruction in such low-field imaging with B0-inhomogeneity compensation under a wide range of various environmental conditions.

Reconstructing hyperspectral images of textiles from a single RGB image utilizing the multihead self-attention mechanism

Hyperspectral images possess abundant information and play a pivotal role in enhancing the accuracy of color difference detection in textiles. However, traditional hyperspectral imaging methods necessitate costly equipment and intricate operational procedures. A novel deep learning model based on a multihead attention mechanism was proposed in this article to facilitate the extensive application of hyperspectral imaging technology in textile quality inspection. This model enabled the reconstruction of the hyperspectral information of plain weave textiles from a single RGB image. In this model, encoder-decoder architecture and pyramid pooling convolutional operations were employed to integrate multiscale features of plain weave cotton-linen textiles. This could capture details and contextual information in textile images more precisely, enhancing the accuracy of hyperspectral image reconstruction. Simultaneously, an attention mechanism was introduced to increase the model’s receptive field and improve its focus on key regions in the input image and feature maps. This resulted in a reduced weighting of redundant information during network learning, leading to an improved feature extraction capability of the network. Through these methods, successful reconstructions of plain weave textiles hyperspectral information from a single RGB image was achieved. Quantitative and qualitative tests were conducted on two datasets, namely, the NTIRE 2020 dataset and a self-made textile dataset, to evaluate the performance of the proposed method. The approach proposed in this article exhibited promising results on both datasets. Specifically, the reconstructed textile hyperspectral images achieved a root mean square error of 0.0344, a peak signal-to-noise ratio of 29.945, a spectral angle mapper of 3.753, and a structural similarity index measure of 0.955 on the textile dataset. In the reconstructed hyperspectral colorimetric experiment, the maximum value of average color difference was 2.641. These results demonstrate that the method can meet the requirements for textile color measurement applications.

Uncertainty Estimation and Out-of-Distribution Detection for Deep Learning-Based Image Reconstruction Using the Local Lipschitz.

Accurate image reconstruction is at the heart of diagnostics in medical imaging. Supervised deep learning-based approaches have been investigated for solving inverse problems including image reconstruction. However, these trained models encounter unseen data distributions that are widely shifted from training data during deployment. Therefore, it is essential to assess whether a given input falls within the training data distribution. Current uncertainty estimation approaches focus on providing an uncertainty map to radiologists, rather than assessing the training distribution fit. In this work, we propose a method based on the local Lipschitz metric to distinguish out-of-distribution images from in-distribution with an area under the curve of 99.94% for True Positive Rate versus False Positive Rate. We demonstrate a very strong relationship between the local Lipschitz value and mean absolute error (MAE), supported by a Spearman's rank correlation coefficient of 0.8475, to determine an uncertainty estimation threshold for optimal performance. Through the identification of false positives, we demonstrate the local Lipschitz and MAE relationship can guide data augmentation and reduce uncertainty. Our study was validated using the AUTOMAP architecture for sensor-to-image Magnetic Resonance Imaging (MRI) reconstruction. We demonstrate our approach outperforms baseline techniques of Monte-Carlo dropout and deep ensembles as well as the state-of-the-art Mean Variance Estimation network approach. We expand our application scope to MRI denoising and Computed Tomography sparse-to-full view reconstructions using UNET architectures. We show our approach is applicable to various architectures and applications, especially in medical imaging, where preserving diagnostic accuracy of reconstructed images remains paramount.

3D-Aligner: An advanced computational tool designed to correct image distortion in expansion microscopy for precise 3D reconstitution and quantitative analysis.

Expansion Microscopy (ExM) is an innovative and cost-effective super-resolution microscopy technique that has become popular in cell biology research. It achieves super-resolution by physically expanding specimens. Since its introduction, ExM has undergone continuous methodological developments to enhance its resolution and labeling capabilities. However, ExM imaging often encounters sample drift during image acquisition due to the physical movement of the expanded hydrogel, posing a significant challenge for accurate image reconstruction. Despite many proposed experimental solutions to mitigate sample drift, a universal solution has yet to be established. In response to this challenge, we developed 3D-Aligner, an advanced and user-friendly image analysis tool designed to computationally correct drift in ExM images for precise three-dimensional image reconstruction and downstream quantification. We demonstrate that 3D-Aligner effectively determines and corrects drift in ExM images with different expansion rates and various fluorescently labeled biological targets, showcasing its capabilities and robustness in drift correction. Additionally, we validate the precision of 3D-Aligner by comparing drift values across different labeled targets and highlight the importance of drift correction in quantification of biological structures.

Towards large-scale single-shot millimeter-wave imaging for low-cost security inspection

Millimeter-Wave (MMW) imaging is a promising technique for contactless security inspection. However, the high cost of requisite large-scale antenna arrays hinders its widespread application in high-throughput scenarios. Here, we report a large-scale single-shot MMW imaging framework, achieving low-cost high-fidelity security inspection. We first analyzed the statistical ranking of each array element through 1934 full-sampled MMW echoes. The highest-ranked elements are preferentially selected based on the ranking, building the experimentally optimal sparse sampling strategy that reduces antenna array cost by one order of magnitude. Additionally, we derived an untrained interpretable learning scheme, realizing robust and accurate MMW image reconstruction from sparsely sampled echoes. Last, we developed a neural network for automatic object detection, and experimentally demonstrated successful detection of concealed centimeter-sized targets using 10% sparse array, whereas all the other contemporary approaches failed at such a low sampling ratio. With the strong detection ability and order-of-magnitude cost reduction, we anticipate that this technique provides a practical way for large-scale single-shot MMW imaging.

Compression and encryption for remote sensing image based on PSO-BP and 2D-MCCM

In response to the large size of remote sensing images and the limitations of existing image compression and encryption algorithms, this paper proposes a novel compression and encryption algorithm. The proposed algorithm utilizes a new type of memristive chaotic mapping in combination with PSO-BP neural networks and multi-threaded parallelism. Specifically, the proposed novel two-dimensional memristive chaotic mapping involves a combination of new memristors based on HP memristors and Cubic chaotic mapping. Compared to existing chaotic systems, this method exhibits stronger randomness and hyperchaotic characteristics. Additionally, to improve the reconstruction accuracy of compressed images, a traditional BP neural network with an added hidden layer is combined with the PSO algorithm for image compression and reconstruction. Furthermore, to enhance the encryption efficiency of remote sensing images, a multi-threaded parallel encryption method is employed, enabling simultaneous permutation within and among threads. Experimental results demonstrate that the proposed algorithm achieves good compression reconstruction accuracy, excellent encryption performance, and resistance to attacks.

A greedy regularized block Kaczmarz method for accelerating reconstruction in magnetic particle imaging

Objective. Magnetic particle imaging (MPI) is an emerging medical tomographic imaging modality that enables real-time imaging with high sensitivity and high spatial and temporal resolution. For the system matrix reconstruction method, the MPI reconstruction problem is an ill-posed inverse problem that is commonly solved using the Kaczmarz algorithm. However, the high computation time of the Kaczmarz algorithm, which restricts MPI reconstruction speed, has limited the development of potential clinical applications for real-time MPI. In order to achieve fast reconstruction in real-time MPI, we propose a greedy regularized block Kaczmarz method (GRBK) which accelerates MPI reconstruction. Approach. GRBK is composed of a greedy partition strategy for the system matrix, which enables preprocessing of the system matrix into well-conditioned blocks to facilitate the convergence of the block Kaczmarz algorithm, and a regularized block Kaczmarz algorithm, which enables fast and accurate MPI image reconstruction at the same time. Main results. We quantitatively evaluated our GRBK using simulation data from three phantoms at 20 dB, 30 dB, and 40 dB noise levels. The results showed that GRBK can improve reconstruction speed by single orders of magnitude compared to the prevalent regularized Kaczmarz algorithm including Tikhonov regularization, the non-negative Fused Lasso, and wavelet-based sparse model. We also evaluated our method on OpenMPIData, which is real MPI data. The results showed that our GRBK is better suited for real-time MPI reconstruction than current state-of-the-art reconstruction algorithms in terms of reconstruction speed as well as image quality. Significance. Our proposed method is expected to be the preferred choice for potential applications of real-time MPI.

Navigating challenges and solutions in quantitative photoacoustic imaging

Photoacoustic imaging, an emerging modality that seamlessly combines advantages of optical absorption contrast and ultrasound resolution, holds great promise for noninvasive imaging of biological tissues. Its applications span across diverse fields, such as dermatology, oncology, cardiology, and neurology. However, achieving accurate image reconstruction and physiological parameters quantification from raw photoacoustic signals presents a significant challenge. This challenge primarily arises from the inherent heterogeneity of tissues, encompassing variations in optical fluence and acoustic properties. In addition, incomplete information acquired from a limited view also leads to artifacts, image distortions, and reduced spatial resolution. Furthermore, robust spectral unmixing approach is another key step to restore the initial biochemical components' distribution with complex or unknown background absorption. To overcome these hurdles, researchers have proposed numerous state-of-the-art techniques, aiming to improve the accuracy and reliability of quantitative photoacoustic imaging (qPAI) in heterogeneous tissue. This review aims to comprehensively overview recent developments over the past decade, for addressing four main challenges frequently encountered in qPAI: limited-view reconstruction, acoustic heterogeneity, optical fluence fluctuations, and robust spectral unmixing, which serves as a reference for readers seeking to understand the specific challenges and corresponding solutions in this field.

Unwrapping non-locality in the image transmission through turbid media

Achieving high-fidelity image transmission through turbid media is a significant challenge facing both the AI and photonic/optical communities. While this capability holds promise for a variety of applications, including data transfer, neural endoscopy, and multi-mode optical fiber-based imaging, conventional deep learning methods struggle to capture the nuances of light propagation, leading to weak generalization and limited reconstruction performance. To address this limitation, we investigated the non-locality present in the reconstructed images and discovered that conventional deep learning methods rely on specific features extracted from the training dataset rather than meticulously reconstructing each pixel. This suggests that they fail to effectively capture long-range dependencies between pixels, which are crucial for accurate image reconstruction. Inspired by the physics of light propagation in turbid media, we developed a global attention mechanism to approach this problem from a broader perspective. Our network harnesses information redundancy generated by peculiar non-local features across the input and output fiber facets. This mechanism enables a two-order-of-magnitude performance boost and high fidelity to the data context, ensuring an accurate representation of intricate details in a pixel-to-pixel reconstruction rather than mere loss minimization.

Masked cross-domain self-supervised deep learning framework for photoacoustic computed tomography reconstruction

Accurate image reconstruction is crucial for photoacoustic (PA) computed tomography (PACT). Recently, deep learning has been used to reconstruct PA images with a supervised scheme, which requires high-quality images as ground truth labels. However, practical implementations encounter inevitable trade-offs between cost and performance due to the expensive nature of employing additional channels for accessing more measurements. Here, we propose a masked cross-domain self-supervised (CDSS) reconstruction strategy to overcome the lack of ground truth labels from limited PA measurements. We implement the self-supervised reconstruction in a model-based form. Simultaneously, we take advantage of self-supervision to enforce the consistency of measurements and images across three partitions of the measured PA data, achieved by randomly masking different channels. Our findings indicate that dynamically masking a substantial proportion of channels, such as 80%, yields meaningful self-supervisors in both the image and signal domains. Consequently, this approach reduces the multiplicity of pseudo solutions and enables efficient image reconstruction using fewer PA measurements, ultimately minimizing reconstruction error. Experimental results on in-vivo PACT dataset of mice demonstrate the potential of our self-supervised framework. Moreover, our method exhibits impressive performance, achieving a structural similarity index (SSIM) of 0.87 in an extreme sparse case utilizing only 13 channels, which outperforms the performance of the supervised scheme with 16 channels (0.77 SSIM). Adding to its advantages, our method can be deployed on different trainable models in an end-to-end manner, further enhancing its versatility and applicability.

Accurate Reconstruction of Multiple Basis Images Directly From Dual Energy CT Data.

We develop optimization-based algorithms to accurately reconstruct multiple ( 2) basis images directly from dual-energy (DE) data in CT. In medical and industrial CT imaging, some basis materials such as bone, metals, and contrast agents of interest are confined often spatially within regions in the image. Exploiting this observation, we develop an optimization-based algorithm to reconstruct, directly from DE data, basis-region images from which multiple ( 2) basis images and virtual monochromatic images (VMIs) can be obtained over the entire image array. We conduct experimental studies using simulated and real DE data in CT, and evaluate basis images and VMIs obtained in terms of visual inspection and quantitative metrics. The study results reveal that the algorithm developed can accurately and robustly reconstruct multiple ( 2) basis images directly from DE data. The developed algorithm can yield accurate multiple ( 2) basis images, VMIs, and physical quantities of interest from DE data in CT. The work may provide insights into the development of practical procedures for reconstructing multiple basis images, VMIs, and physical quantities from DE data in applications. The work can be extended to reconstruct multiple basis images in multi-spectral or photon-counting CT.

GPU-accelerated parallel image reconstruction strategies for magnetic particle imaging

Objective. Image reconstruction is a fundamental step in magnetic particle imaging (MPI). One of the main challenges is the fact that the reconstructions are computationally intensive and time-consuming, so choosing an algorithm presents a compromise between accuracy and execution time, which depends on the application. This work proposes a method that provides both fast and accurate image reconstructions. Approach. Image reconstruction algorithms were implemented to be executed in parallel in graphics processing units (GPUs) using the CUDA framework. The calculation of the model-based MPI calibration matrix was also implemented in GPU to allow both fast and flexible reconstructions. Main results. The parallel algorithms were able to accelerate the reconstructions by up to about 6,100 times in comparison to the serial Kaczmarz algorithm executed in the CPU, allowing for real-time applications. Reconstructions using the OpenMPIData dataset validated the proposed algorithms and demonstrated that they are able to provide both fast and accurate reconstructions. The calculation of the calibration matrix was accelerated by up to about 37 times. Significance. The parallel algorithms proposed in this work can provide single-frame MPI reconstructions in real time, with frame rates greater than 100 frames per second. The parallel calculation of the calibration matrix can be combined with the parallel reconstruction to deliver images in less time than the serial Kaczmarz reconstruction, potentially eliminating the need of storing the calibration matrix in the main memory, and providing the flexibility of redefining scanning and reconstruction parameters during execution.

Dual-channel end-to-end network with prior knowledge embedding for improving spatial resolution of magnetic particle imaging

Magnetic particle imaging (MPI) is an emerging non-invasive medical imaging tomography technology based on magnetic particles, with excellent imaging depth penetration, high sensitivity and contrast. Spatial resolution and signal-to-noise ratio (SNR) are key performance metrics for evaluating MPI, which are directly influenced by the gradient of the selection field (SF). Increasing the SF gradient can improve the spatial resolution of MPI, but will lead to a decrease in SNR. Deep learning (DL) methods may enable obtaining high-resolution images from low-resolution images to improve the MPI resolution under low gradient conditions. However, existing DL methods overlook the physical procedures contributing to the blurring of MPI images, resulting in low interpretability and hindering breakthroughs in resolution. To address this issue, we propose a dual-channel end-to-end network with prior knowledge embedding for MPI (DENPK-MPI) to effectively establish a latent mapping between low-gradient and high-gradient images, thus improving MPI resolution without compromising SNR. By seamlessly integrating MPI PSF with DL paradigm, DENPK-MPI leads to a significant improvement in spatial resolution performance. Simulation, phantom, and in vivo MPI experiments have collectively confirmed that our method can improve the resolution of low-gradient MPI images without sacrificing SNR, resulting in a decrease in full width at half maximum by 14.8%–23.8 %, and the accuracy of image reconstruction is 18.2 %–27.3 % higher than other DL methods. In conclusion, we propose a DL method that incorporates MPI prior knowledge, which can improve the spatial resolution of MPI without compromising SNR and possess improved biomedical application.

Learning-based sound speed estimation and aberration correction for linear-array photoacoustic imaging

Photoacoustic (PA) image reconstruction involves acoustic inversion that necessitates the specification of the speed of sound (SoS) within the medium of propagation. Due to the lack of information on the spatial distribution of the SoS within heterogeneous soft tissue, a homogeneous SoS distribution (such as 1540 m/s) is typically assumed in PA image reconstruction, similar to that of ultrasound (US) imaging. Failure to compensate for the SoS variations leads to aberration artefacts, deteriorating the image quality. Various methods have been proposed to address this issue, but they usually involve complex hardware and/or time-consuming algorithms, hindering clinical translation. In this work, we introduce a deep learning framework for SoS estimation and subsequent aberration correction in a dual-modal PA/US imaging system exploiting a clinical US probe. As the acquired PA and US images were inherently co-registered, the estimated SoS distribution from US channel data using a deep neural network was incorporated for accurate PA image reconstruction. The framework comprised an initial pre-training stage based on digital phantoms, which was further enhanced through transfer learning using physical phantom data and associated SoS maps obtained from measurements. This framework achieved a root mean square error of 10.2 m/s and 15.2 m/s for SoS estimation on digital and physical phantoms, respectively and structural similarity index measures of up to 0.88 for PA reconstructions compared to the conventional approach of 0.69. A maximum of 1.2 times improvement in the signal-to-noise ratio of PA images was further demonstrated with a human volunteer study. Our results show that the proposed framework could be valuable in various clinical and preclinical applications to enhance PA image reconstruction.

Magnetic resonance image reconstruction based on image decomposition constrained by total variation and tight frame.

Magnetic resonance imaging (MRI) is a commonly used tool in clinical medicine, but it suffers from the disadvantage of slow imaging speed. To address this, we propose a novel MRI reconstruction algorithm based on image decomposition to realize accurate image reconstruction with undersampled k-space data. In our algorithm, the MR images to be recovered are split into cartoon and texture components utilizing image decomposition theory. Different sparse transform constraints are applied to each component based on their morphological structure characteristics. The total variation transform constraint is used for the smooth cartoon component, while the L0 norm constraint of tight frame redundant transform is used for the oscillatory texture component. Finally, an alternating iterative minimization approach is adopted to complete the reconstruction. Numerous numerical experiments are conducted on several MR images and the results consistently show that, compared with the existing classical compressed sensing algorithm, our algorithm significantly improves the peak signal-to-noise ratio of the reconstructed images and preserves more image details. Our algorithm harnesses the sparse characteristics of different image components to reconstruct MR images accurately with highly undersampled data. It can greatly accelerate MRI speed and be extended to other imaging reconstruction fields.

Reconstruction from CT truncated data based on dual-domain transformer coupled feature learning

To propose a CT truncated data reconstruction model (DDTrans) based on projection and image dualdomain Transformer coupled feature learning for reducing truncation artifacts and image structure distortion caused by insufficient field of view (FOV) in CT scanning. Transformer was adopted to build projection domain and image domain restoration models, and the long-range dependency modeling capability of the Transformer attention module was used to capture global structural features to restore the projection data information and enhance the reconstructed images. We constructed a differentiable Radon back-projection operator layer between the projection domain and image domain networks to enable end-to-end training of DDTrans. Projection consistency loss was introduced to constrain the image forwardprojection results to further improve the accuracy of image reconstruction. The experimental results with Mayo simulation data showed that for both partial truncation and interior scanning data, the proposed DDTrans method showed better performance than the comparison algorithms in removing truncation artifacts at the edges and restoring the external information of the FOV. The DDTrans method can effectively remove CT truncation artifacts to ensure accurate reconstruction of the data within the FOV and achieve approximate reconstruction of data outside the FOV.

A new ECT image reconstruction algorithm based on Vision transformer (ViT)

Aiming at the problem of low accuracy of ECT image reconstruction, this paper proposes an ECT image reconstruction algorithm based on Vision Transformer (ViT). ViT is a method that applies the Transformer to the field of image classification, which is characterized by strong long-distance dependency learning ability and strong multi-modal fusion ability compared to CNN. This paper fully utilizes the characteristics of ViT to transform the image reconstruction process of ECT into the classification process of ViT. Here, a method is proposed to use the object field distribution as the image classification label. This method converts a two-dimensional image of the object field distribution into a one-dimensional vector, which is the label vector of the image classification. These vectors and their corresponding reconstructed images obtained by the Landweber algorithm form the sample set of ViT. Extracting a large number of flow pattern samples with various shapes and distributions through COMSOL is used as a training set. After training ViT, this network model is used to infer the labels of the predicted flow patterns. After post-processing this label, the corresponding reconstructed image can be obtained. Finally, simulation experiments are conducted, and the experiments results show that the image errors and correlation coefficients of the reconstructed images obtained through the algorithm in this paper are better than those of Tikhonov algorithm, Landweber algorithm and Long Short-Term Memory Network(LSTM). And this algorithm has better resistance to noise interference than Tikhonov algorithm, Landweber algorithm, and LSTM. This also provides a new approach and means for ECT image reconstruction.

Accelerating cardiac diffusion tensor imaging using Swin transformer with octave convolution

AbstractCardiac diffusion tensor imaging (cDTI) is a promising and noninvasive magnetic resonance imaging (MRI) technique for assessing myocardial fiber microstructure. However, its clinical application is hampered by lengthy scanning and susceptibility to motion artifacts. This study proposes a cDTI reconstruction model (OSDTI), which leverages octave convolution (OctConv) and Swin Transformer to reconstruct diffusion‐weighted (DW) images from undersampled k‐space data. Our model capitalizes on the strengths of both OctConv and Swin Transformers. Specifically, the OctConv module excels at capturing intricate details and texture information within DW images, while the residual‐connected Swin Transformer module facilitates information retention across various feature extraction stages, thereby enhancing overall image comprehension and reconstruction accuracy. The evaluation of OSDTI using a human ex vivo heart dataset robustly validated the generalization ability of the model. Comparative analyze against existing deep‐learning methods demonstrated OSDTI's superior performance in both DW image quality and diffusion tensor metrics.

Compressed Sensing for Biomedical Photoacoustic Imaging: A Review.

Photoacoustic imaging (PAI) is a rapidly developing emerging non-invasive biomedical imaging technique that combines the strong contrast from optical absorption imaging and the high resolution from acoustic imaging. Abnormal biological tissues (such as tumors and inflammation) generate different levels of thermal expansion after absorbing optical energy, producing distinct acoustic signals from normal tissues. This technique can detect small tissue lesions in biological tissues and has demonstrated significant potential for applications in tumor research, melanoma detection, and cardiovascular disease diagnosis. During the process of collecting photoacoustic signals in a PAI system, various factors can influence the signals, such as absorption, scattering, and attenuation in biological tissues. A single ultrasound transducer cannot provide sufficient information to reconstruct high-precision photoacoustic images. To obtain more accurate and clear image reconstruction results, PAI systems typically use a large number of ultrasound transducers to collect multi-channel signals from different angles and positions, thereby acquiring more information about the photoacoustic signals. Therefore, to reconstruct high-quality photoacoustic images, PAI systems require a significant number of measurement signals, which can result in substantial hardware and time costs. Compressed sensing is an algorithm that breaks through the Nyquist sampling theorem and can reconstruct the original signal with a small number of measurement signals. PAI based on compressed sensing has made breakthroughs over the past decade, enabling the reconstruction of low artifacts and high-quality images with a small number of photoacoustic measurement signals, improving time efficiency, and reducing hardware costs. This article provides a detailed introduction to PAI based on compressed sensing, such as the physical transmission model-based compressed sensing method, two-stage reconstruction-based compressed sensing method, and single-pixel camera-based compressed sensing method. Challenges and future perspectives of compressed sensing-based PAI are also discussed.

Quaternion fast and accurate polar harmonic Fourier moments for color image analysis and object recognition

Image moments, as a kind of global feature descriptor of images, have become a valuable tool for pattern recognition and image analysis. However, traditional methods are mainly used to deal with grayscale images. In this paper, we apply quaternions to fast and accurate polar harmonic Fourier moments, proposing a kind of quaternion fast and accurate polar harmonic Fourier moment (QFAPHFM) capable of handling color images. Furthermore, this paper provides a detailed analysis of the invariance of QFAPHFMs under rotation, scaling, and translation transformations. The experimental results show that QFAPHFMs exhibit excellent performance in both image reconstruction and object recognition tasks. QFAPHFMs achieve accurate image reconstruction under noiseless and noisy conditions, and demonstrate excellent recognition performance in the color-based object recognition tasks.