IVMay 2
A Target-Free Harmonization Method for MRIMinjun Kim, Dong Ju Mun, Hwihun Jeong et al.
In MRI, variations in scan parameters, sequence, or hardware can lead to discrepancies in image appearance, even for the same subject. These inconsistencies, known as domain shifts, can hinder image analysis and degrade the performance of deep learning models trained on data from specific target domains. MRI image harmonization aims to address these issues by aligning source domain images to the target domain images while preserving biological information such as anatomical structures. However, most existing harmonization approaches require access to both source and target domain data in training or test time. This dependence induces data sharing between institutions, raising concerns about patient privacy and substantially limiting the harmonization approaches that can be practically deployed in clinical settings. To overcome these limitations, we introduce TgtFreeHarmony, the harmonization framework tailored for target-free scenarios, eliminating the need for target domain data and any data sharing, enabling privacy-preserving harmonization directly within the source institution. Our approach estimates the target domain style by searching the manifold of MRI domain style constructed via a disentanglement-based generator using Bayesian optimization guided by the performance of a downstream task model, which is trained on target domain data. We evaluated our method on the brain tissue segmentation task across multiple institutes and demonstrated that it effectively harmonizes source images into target images, leading to improved downstream task performance. By enabling harmonization without any access to target-domain data, TgtFreeHarmony establishes a new direction of harmonization preserving data privacy that can be realistically deployed within clinical environments.
IVSep 16, 2024Code
MOST: MR reconstruction Optimization for multiple downStream Tasks via continual learningHwihun Jeong, Se Young Chun, Jongho Lee
Deep learning-based Magnetic Resonance (MR) reconstruction methods have focused on generating high-quality images but often overlook the impact on downstream tasks (e.g., segmentation) that utilize the reconstructed images. Cascading separately trained reconstruction network and downstream task network has been shown to introduce performance degradation due to error propagation and domain gaps between training datasets. To mitigate this issue, downstream task-oriented reconstruction optimization has been proposed for a single downstream task. Expanding this optimization to multi-task scenarios is not straightforward. In this work, we extended this optimization to sequentially introduced multiple downstream tasks and demonstrated that a single MR reconstruction network can be optimized for multiple downstream tasks by deploying continual learning (MOST). MOST integrated techniques from replay-based continual learning and image-guided loss to overcome catastrophic forgetting. Comparative experiments demonstrated that MOST outperformed a reconstruction network without finetuning, a reconstruction network with naïve finetuning, and conventional continual learning methods. The source code is available at: https://github.com/SNU-LIST/MOST.
IVDec 16, 2025
Deep learning water-unsuppressed MRSI at ultra-high field for simultaneous quantitative metabolic, susceptibility and myelin water imagingPaul J. Weiser, Jiye Kim, Jongho Lee et al.
Purpose: Magnetic Resonance Spectroscopic Imaging (MRSI) maps endogenous brain metabolism while suppressing the overwhelming water signal. Water-unsuppressed MRSI (wu-MRSI) allows simultaneous imaging of water and metabolites, but large water sidebands cause challenges for metabolic fitting. We developed an end-to-end deep-learning pipeline to overcome these challenges at ultra-high field. Methods:Fast high-resolution wu-MRSI was acquired at 7T with non-cartesian ECCENTRIC sampling and ultra-short echo time. A water and lipid removal network (WALINET+) was developed to remove lipids, water signal, and sidebands. MRSI reconstruction was performed by DeepER and a physics-informed network for metabolite fitting. Water signal was used for absolute metabolite quantification, quantitative susceptibility mapping (QSM), and myelin water fraction imaging (MWF). Results: WALINET+ provided the lowest NRMSE (< 2%) in simulations and in vivo the smallest bias (< 20%) and limits-of-agreement (+-63%) between wu-MRSI and ws-MRSI scans. Several metabolites such as creatine and glutamate showed higher SNR in wu-MRSI. QSM and MWF obtained from wu-MRSI and GRE showed good agreement with 0 ppm/5.5% bias and +-0.05 ppm/ +- 12.75% limits-of-agreement. Conclusion: High-quality metabolic, QSM, and MWF mapping of the human brain can be obtained simultaneously by ECCENTRIC wu-MRSI at 7T with 2 mm isotropic resolution in 12 min. WALINET+ robustly removes water sidebands while preserving metabolite signal, eliminating the need for water suppression and separate water acquisitions.
IVAug 16, 2022
Self-supervised training of deep denoisers in multi-coil MRI considering noise correlationsJuhyung Park, Dongwon Park, Sooyeon Ji et al.
Deep learning-based denoising methods have shown powerful results for improving the signal-to-noise ratio of magnetic resonance (MR) images, mostly by leveraging supervised learning with clean ground truth. However, acquiring clean ground truth images is often expensive and time-consuming. Self supervised methods have been widely investigated to mitigate the dependency on clean images, but mostly rely on the suboptimal splitting of K-space measurements of an image to yield input and target images for ensuring statistical independence. In this study, we investigate an alternative self-supervised training method for deep denoisers in multi-coil MRI, dubbed Coil2Coil (C2C), that naturally split and combine the multi-coil data among phased array coils, generating two noise-corrupted images for training. This novel approach allows exploiting multi-coil redundancy, but the images are statistically correlated and may not have the same clean image. To mitigate these issues, we propose the methods to pproximately decorrelate the statistical dependence of these images and match the underlying clean images, thus enabling them to be used as the training pairs. For synthetic denoising experiments, C2C yielded the best performance against prior self-supervised methods, reporting outcome comparable even to supervised methods. For real-world denoising cases, C2C yielded consistent performance as synthetic cases, removing only noise structures.
CLJan 5, 2025Code
Multi-LLM Collaborative Caption Generation in Scientific DocumentsJaeyoung Kim, Jongho Lee, Hong-Jun Choi et al.
Scientific figure captioning is a complex task that requires generating contextually appropriate descriptions of visual content. However, existing methods often fall short by utilizing incomplete information, treating the task solely as either an image-to-text or text summarization problem. This limitation hinders the generation of high-quality captions that fully capture the necessary details. Moreover, existing data sourced from arXiv papers contain low-quality captions, posing significant challenges for training large language models (LLMs). In this paper, we introduce a framework called Multi-LLM Collaborative Figure Caption Generation (MLBCAP) to address these challenges by leveraging specialized LLMs for distinct sub-tasks. Our approach unfolds in three key modules: (Quality Assessment) We utilize multimodal LLMs to assess the quality of training data, enabling the filtration of low-quality captions. (Diverse Caption Generation) We then employ a strategy of fine-tuning/prompting multiple LLMs on the captioning task to generate candidate captions. (Judgment) Lastly, we prompt a prominent LLM to select the highest quality caption from the candidates, followed by refining any remaining inaccuracies. Human evaluations demonstrate that informative captions produced by our approach rank better than human-written captions, highlighting its effectiveness. Our code is available at https://github.com/teamreboott/MLBCAP
AIApr 16
Sequence Search: Automated Sequence Design using Neural Architecture SearchRokgi Hong, Hongjun An, Sooyeon Ji et al.
Developing an MR sequence is challenging and remains largely constrained by human intuition. Recently, AI-driven approaches have been proposed; however, most require an initial sequence for parameter optimization or extensive training datasets, limiting their general applicability. In this study, we propose "Sequence Search," an automated sequence design framework based on neural architecture search. The method takes tissue properties, imaging parameters, and design objectives as inputs and generates pulse sequences satisfying the design objectives, without requiring prior knowledge of conventional sequence structures. Sequence Search iteratively generates candidate sequences through neural architecture search and optimizes them via a differentiable Bloch simulator and objective-specific loss functions using gradient-based learning. The framework successfully replicated conventional spin-echo, T2-weighted spin-echo, and inversion recovery sequences. Less intuitive solutions were also discovered, such as three-RF spin-echo-like sequences with reduced RF energy and refocusing phases deviating from the conventional Hahn-echo. This work establishes a generalizable framework for automated MR sequence design, highlighting the potential to explore configurations beyond conventional designs based on human intuition.
IVMay 18, 2023Code
BlindHarmony: "Blind" Harmonization for MR Images via Flow modelHwihun Jeong, Heejoon Byun, Dong Un Kang et al.
In MRI, images of the same contrast (e.g., T$_1$) from the same subject can exhibit noticeable differences when acquired using different hardware, sequences, or scan parameters. These differences in images create a domain gap that needs to be bridged by a step called image harmonization, to process the images successfully using conventional or deep learning-based image analysis (e.g., segmentation). Several methods, including deep learning-based approaches, have been proposed to achieve image harmonization. However, they often require datasets from multiple domains for deep learning training and may still be unsuccessful when applied to images from unseen domains. To address this limitation, we propose a novel concept called `Blind Harmonization', which utilizes only target domain data for training but still has the capability to harmonize images from unseen domains. For the implementation of blind harmonization, we developed BlindHarmony using an unconditional flow model trained on target domain data. The harmonized image is optimized to have a correlation with the input source domain image while ensuring that the latent vector of the flow model is close to the center of the Gaussian distribution. BlindHarmony was evaluated on both simulated and real datasets and compared to conventional methods. BlindHarmony demonstrated noticeable performance on both datasets, highlighting its potential for future use in clinical settings. The source code is available at: https://github.com/SNU-LIST/BlindHarmony
IVSep 18, 2024
Adaptive Selection of Sampling-Reconstruction in Fourier Compressed SensingSeongmin Hong, Jaehyeok Bae, Jongho Lee et al.
Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. However, traditional optimization-based reconstruction is slow and can not yield an exact image in practice. Deep learning-based reconstruction has been a promising alternative to optimization-based reconstruction, outperforming it in accuracy and computation speed. Finding an efficient sampling method with deep learning-based reconstruction, especially for Fourier CS remains a challenge. Existing joint optimization of sampling-reconstruction works ($\mathcal{H}_1$) optimize the sampling mask but have low potential as it is not adaptive to each data point. Adaptive sampling ($\mathcal{H}_2$) has also disadvantages of difficult optimization and Pareto sub-optimality. Here, we propose a novel adaptive selection of sampling-reconstruction ($\mathcal{H}_{1.5}$) framework that selects the best sampling mask and reconstruction network for each input data. We provide theorems that our method has a higher potential than $\mathcal{H}_1$ and effectively solves the Pareto sub-optimality problem in sampling-reconstruction by using separate reconstruction networks for different sampling masks. To select the best sampling mask, we propose to quantify the high-frequency Bayesian uncertainty of the input, using a super-resolution space generation model. Our method outperforms joint optimization of sampling-reconstruction ($\mathcal{H}_1$) and adaptive sampling ($\mathcal{H}_2$) by achieving significant improvements on several Fourier CS problems.
CLApr 22, 2024
RTP-LX: Can LLMs Evaluate Toxicity in Multilingual Scenarios?Adrian de Wynter, Ishaan Watts, Tua Wongsangaroonsri et al. · cmu, deepmind
Large language models (LLMs) and small language models (SLMs) are being adopted at remarkable speed, although their safety still remains a serious concern. With the advent of multilingual S/LLMs, the question now becomes a matter of scale: can we expand multilingual safety evaluations of these models with the same velocity at which they are deployed? To this end, we introduce RTP-LX, a human-transcreated and human-annotated corpus of toxic prompts and outputs in 28 languages. RTP-LX follows participatory design practices, and a portion of the corpus is especially designed to detect culturally-specific toxic language. We evaluate 10 S/LLMs on their ability to detect toxic content in a culturally-sensitive, multilingual scenario. We find that, although they typically score acceptably in terms of accuracy, they have low agreement with human judges when scoring holistically the toxicity of a prompt; and have difficulty discerning harm in context-dependent scenarios, particularly with subtle-yet-harmful content (e.g. microaggressions, bias). We release this dataset to contribute to further reduce harmful uses of these models and improve their safe deployment.
LGApr 7, 2024
A Note on LoRAVlad Fomenko, Han Yu, Jongho Lee et al.
LoRA (Low-Rank Adaptation) has emerged as a preferred method for efficiently adapting Large Language Models (LLMs) with remarkable simplicity and efficacy. This note extends the original LoRA paper by offering new perspectives that were not initially discussed and presents a series of insights for deploying LoRA at scale. Without introducing new experiments, we aim to improve the understanding and application of LoRA.
LGFeb 15, 2024
QUICK: Quantization-aware Interleaving and Conflict-free Kernel for efficient LLM inferenceTaesu Kim, Jongho Lee, Daehyun Ahn et al.
We introduce QUICK, a group of novel optimized CUDA kernels for the efficient inference of quantized Large Language Models (LLMs). QUICK addresses the shared memory bank-conflict problem of state-of-the-art mixed precision matrix multiplication kernels. Our method interleaves the quantized weight matrices of LLMs offline to skip the shared memory write-back after the dequantization. We demonstrate up to 1.91x speedup over existing kernels of AutoAWQ on larger batches and up to 1.94x throughput gain on representative LLM models on various NVIDIA GPU devices.
CVOct 22, 2025
Predicting before Reconstruction: A generative prior framework for MRI accelerationJuhyung Park, Rokgi Hong, Roh-Eul Yoo et al.
Recent advancements in artificial intelligence have created transformative capabilities in image synthesis and generation, enabling diverse research fields to innovate at revolutionary speed and spectrum. In this study, we leverage this generative power to introduce a new paradigm for accelerating Magnetic Resonance Imaging (MRI), introducing a shift from image reconstruction to proactive predictive imaging. Despite being a cornerstone of modern patient care, MRI's lengthy acquisition times limit clinical throughput. Our novel framework addresses this challenge by first predicting a target contrast image, which then serves as a data-driven prior for reconstructing highly under-sampled data. This informative prior is predicted by a generative model conditioned on diverse data sources, such as other contrast images, previously scanned images, acquisition parameters, patient information. We demonstrate this approach with two key applications: (1) reconstructing FLAIR images using predictions from T1w and/or T2w scans, and (2) reconstructing T1w images using predictions from previously acquired T1w scans. The framework was evaluated on internal and multiple public datasets (total 14,921 scans; 1,051,904 slices), including multi-channel k-space data, for a range of high acceleration factors (x4, x8 and x12). The results demonstrate that our prediction-prior reconstruction method significantly outperforms other approaches, including those with alternative or no prior information. Through this framework we introduce a fundamental shift from image reconstruction towards a new paradigm of predictive imaging.
CLSep 30, 2025
Personalized Scientific Figure Caption Generation: An Empirical Study on Author-Specific Writing Style TransferJaeyoung Kim, Jongho Lee, Hongjun Choi et al.
We study personalized figure caption generation using author profile data from scientific papers. Our experiments demonstrate that rich author profile data, combined with relevant metadata, can significantly improve the personalization performance of multimodal large language models. However, we also reveal a fundamental trade-off between matching author style and maintaining caption quality. Our findings offer valuable insights and future directions for developing practical caption automation systems that balance both objectives. This work was conducted as part of the 3rd SciCap challenge.
IVApr 30, 2025
Efficient and robust 3D blind harmonization for large domain gapsHwihun Jeong, Hayeon Lee, Se Young Chun et al.
Blind harmonization has emerged as a promising technique for MR image harmonization to achieve scale-invariant representations, requiring only target domain data (i.e., no source domain data necessary). However, existing methods face limitations such as inter-slice heterogeneity in 3D, moderate image quality, and limited performance for a large domain gap. To address these challenges, we introduce BlindHarmonyDiff, a novel blind 3D harmonization framework that leverages an edge-to-image model tailored specifically to harmonization. Our framework employs a 3D rectified flow trained on target domain images to reconstruct the original image from an edge map, then yielding a harmonized image from the edge of a source domain image. We propose multi-stride patch training for efficient 3D training and a refinement module for robust inference by suppressing hallucination. Extensive experiments demonstrate that BlindHarmonyDiff outperforms prior arts by harmonizing diverse source domain images to the target domain, achieving higher correspondence to the target domain characteristics. Downstream task-based quality assessments such as tissue segmentation and age prediction on diverse MR scanners further confirm the effectiveness of our approach and demonstrate the capability of our robust and generalizable blind harmonization.
CVFeb 3, 2025
Vessel segmentation for X-separationTaechang Kim, Sooyeon Ji, Kyeongseon Min et al.
$χ$-separation is an advanced quantitative susceptibility mapping (QSM) method that is designed to generate paramagnetic ($χ_{para}$) and diamagnetic ($|χ_{dia}|$) susceptibility maps, reflecting the distribution of iron and myelin in the brain. However, vessels have shown artifacts, interfering with the accurate quantification of iron and myelin in applications. To address this challenge, a new vessel segmentation method for $χ$-separation is developed. The method comprises three steps: 1) Seed generation from $\textit{R}_2^*$ and the product of $χ_{para}$ and $|χ_{dia}|$ maps; 2) Region growing, guided by vessel geometry, creating a vessel mask; 3) Refinement of the vessel mask by excluding non-vessel structures. The performance of the method was compared to conventional vessel segmentation methods both qualitatively and quantitatively. To demonstrate the utility of the method, it was tested in two applications: quantitative evaluation of a neural network-based $χ$-separation reconstruction method ($χ$-sepnet-$\textit{R}_2^*$) and population-averaged region of interest (ROI) analysis. The proposed method demonstrates superior performance to the conventional vessel segmentation methods, effectively excluding the non-vessel structures, achieving the highest Dice score coefficient. For the applications, applying vessel masks report notable improvements for the quantitative evaluation of $χ$-sepnet-$\textit{R}_2^*$ and statistically significant differences in population-averaged ROI analysis. These applications suggest excluding vessels when analyzing the $χ$-separation maps provide more accurate evaluations. The proposed method has the potential to facilitate various applications, offering reliable analysis through the generation of a high-quality vessel mask.
IVDec 4, 2023
Fast and accurate sparse-view CBCT reconstruction using meta-learned neural attenuation field and hash-encoding regularizationHeejun Shin, Taehee Kim, Jongho Lee et al.
Cone beam computed tomography (CBCT) is an emerging medical imaging technique to visualize the internal anatomical structures of patients. During a CBCT scan, several projection images of different angles or views are collectively utilized to reconstruct a tomographic image. However, reducing the number of projections in a CBCT scan while preserving the quality of a reconstructed image is challenging due to the nature of an ill-posed inverse problem. Recently, a neural attenuation field (NAF) method was proposed by adopting a neural radiance field algorithm as a new way for CBCT reconstruction, demonstrating fast and promising results using only 50 views. However, decreasing the number of projections is still preferable to reduce potential radiation exposure, and a faster reconstruction time is required considering a typical scan time. In this work, we propose a fast and accurate sparse-view CBCT reconstruction (FACT) method to provide better reconstruction quality and faster optimization speed in the minimal number of view acquisitions ($<$ 50 views). In the FACT method, we meta-trained a neural network and a hash-encoder using a few scans (= 15), and a new regularization technique is utilized to reconstruct the details of an anatomical structure. In conclusion, we have shown that the FACT method produced better, and faster reconstruction results over the other conventional algorithms based on CBCT scans of different body parts (chest, head, and abdomen) and CT vendors (Siemens, Phillips, and GE).
IVMay 7, 2021
Deep reinforcement learning-designed radiofrequency waveform in MRIDongmyung Shin, Younghoon Kim, Chungseok Oh et al.
Carefully engineered radiofrequency (RF) pulses play a key role in a number of systems such as mobile phone, radar, and magnetic resonance imaging. The design of an RF waveform, however, is often posed as an inverse problem with no general solution. As a result, various design methods each with a specific purpose have been developed based on the intuition of human experts. In this work, we propose an artificial intelligence (AI)-powered RF pulse design framework, DeepRF, which utilizes the self-learning characteristics of deep reinforcement learning to generate a novel RF pulse. The effectiveness of DeepRF is demonstrated using four types of RF pulses that are commonly used. The DeepRF-designed pulses successfully satisfy the design criteria while reporting reduced energy. Analyses demonstrate the pulses utilize new mechanisms of magnetization manipulation, suggesting the potentials of DeepRF in discovering unseen design dimensions beyond human intuition. This work may lay the foundation for an emerging field of AI-driven RF waveform design.
IVFeb 4, 2021
DIFFnet: Diffusion parameter mapping network generalized for input diffusion gradient schemes and bvaluesJuhung Park, Woojin Jung, Eun-Jung Choi et al.
In MRI, deep neural networks have been proposed to reconstruct diffusion model parameters. However, the inputs of the networks were designed for a specific diffusion gradient scheme (i.e., diffusion gradient directions and numbers) and a specific b-value that are the same as the training data. In this study, a new deep neural network, referred to as DIFFnet, is developed to function as a generalized reconstruction tool of the diffusion-weighted signals for various gradient schemes and b-values. For generalization, diffusion signals are normalized in a q-space and then projected and quantized, producing a matrix (Qmatrix) as an input for the network. To demonstrate the validity of this approach, DIFFnet is evaluated for diffusion tensor imaging (DIFFnetDTI) and for neurite orientation dispersion and density imaging (DIFFnetNODDI). In each model, two datasets with different gradient schemes and b-values are tested. The results demonstrate accurate reconstruction of the diffusion parameters at substantially reduced processing time (approximately 8.7 times and 2240 times faster processing time than conventional methods in DTI and NODDI, respectively; less than 4% mean normalized root-mean-square errors (NRMSE) in DTI and less than 8% in NODDI). The generalization capability of the networks was further validated using reduced numbers of diffusion signals from the datasets. Different from previously proposed deep neural networks, DIFFnet does not require any specific gradient scheme and b-value for its input. As a result, it can be adopted as an online reconstruction tool for various complex diffusion imaging.
LGSep 29, 2020
Machine-Learning Approach to Analyze the Status of Forklift Vehicles with Irregular Movement in a ShipyardHyeonju Lee, Jongho Lee, Minji An et al.
In large shipyards, the management of equipment, which are used for building a variety of ships, is critical. Because orders vary year to year, shipyard managers are required to determine methods to make the most of their limited resources. A particular difficulty that arises because of the nature and size of shipyards is the management of moving vehicles. In recent years, shipbuilding companies have attempted to manage and track the locations and movements of vehicles using Global Positioning System (GPS) modules. However, because certain vehicles, such as forklifts, roam irregularly around a yard, identifying their working status without being onsite is difficult. Location information alone is not sufficient to determine whether a vehicle is working, moving, waiting, or resting. This study proposes an approach based on machine learning to identify the work status of each forklift. We use the DBSCAN and k-means algorithms to identify the area in which a particular forklift is operating and the type of work it is performing. We developed a business intelligence system to collect information from forklifts equipped with GPS and Internet of Things (IoT) devices. The system provides visual information on the status of individual forklifts and helps in the efficient management of their movements within large shipyards.
LGDec 19, 2019
Deep Reinforcement Learning Designed Shinnar-Le Roux RF Pulse using Root-Flipping: DeepRF_SLRDongmyung Shin, Sooyeon Ji, Doohee Lee et al.
A novel approach of applying deep reinforcement learning to an RF pulse design is introduced. This method, which is referred to as DeepRF_SLR, is designed to minimize the peak amplitude or, equivalently, minimize the pulse duration of a multiband refocusing pulse generated by the Shinar Le-Roux (SLR) algorithm. In the method, the root pattern of SLR polynomial, which determines the RF pulse shape, is optimized by iterative applications of deep reinforcement learning and greedy tree search. When tested for the designs of the multiband factors of three and seven RFs, DeepRF_SLR demonstrated improved performance compared to conventional methods, generating shorter duration RF pulses in shorter computational time. In the experiments, the RF pulse from DeepRF_SLR produced a slice profile similar to the minimum-phase SLR RF pulse and the profiles matched to that of the computer simulation. Our approach suggests a new way of designing an RF by applying a machine learning algorithm, demonstrating a machine-designed MRI sequence.
IVSep 30, 2019
Nonlinear Dipole Inversion (NDI) enables Quantitative Susceptibility Mapping (QSM) without parameter tuningDaniel Polak, Itthi Chatnuntawech, Jaeyeon Yoon et al.
We propose Nonlinear Dipole Inversion (NDI) for high-quality Quantitative Susceptibility Mapping (QSM) without regularization tuning, while matching the image quality of state-of-the-art reconstruction techniques. In addition to avoiding over-smoothing that these techniques often suffer from, we also obviate the need for parameter selection. NDI is flexible enough to allow for reconstruction from an arbitrary number of head orientations, and outperforms COSMOS even when using as few as 1-direction data. This is made possible by a nonlinear forward-model that uses the magnitude as an effective prior, for which we derived a simple gradient descent update rule. We synergistically combine this physics-model with a Variational Network (VN) to leverage the power of deep learning in the VaNDI algorithm. This technique adopts the simple gradient descent rule from NDI and learns the network parameters during training, hence requires no additional parameter tuning. Further, we evaluate NDI at 7T using highly accelerated Wave-CAIPI acquisitions at 0.5 mm isotropic resolution and demonstrate high-quality QSM from as few as 2-direction data.