Real-world image denoising remains a challenge task. This paper studies self-supervised image denoising, requiring only noisy images captured in a single shot. We revamping the blind-spot technique by leveraging the transformer’s capability for long-range pixel interactions, which is crucial for effectively removing noise dependence in relating pixel–a requirement for achieving great performance for the blind-spot technique. The proposed method integrates these elements with two key innovations: a directional self-attention (DSA) module using a halfplane grid for self-attention, creating a sophisticated blind-spot structure, and a Siamese architecture with mutual learning to mitigate the performance impacts from the restricted attention grid in DSA. Experiments on benchmark datasets demonstrate that our method outperforms existing self-supervised and clean-imagefree methods. This combination of blind-spot and transformer techniques provides a natural synergy for tackling real-world image denoising challenges.
Inference-time computation techniques, analogous to human System 2 Thinking, have recently become popular for improving model performances. However, most existing approaches suffer from several limitations: they are modality-specific (e.g., working only in text), problem-specific (e.g., verifiable domains like math and coding), or require additional supervision/training on top of unsupervised pretraining (e.g., verifiers or verifiable rewards). In this paper, we ask the question "Is it possible to generalize these System 2 Thinking approaches, and develop models that learn to think solely from unsupervised learning?" Interestingly, we find the answer is yes, by learning to explicitly verify the compatibility between inputs and candidate-predictions, and then re-framing prediction problems as optimization with respect to this verifier. Specifically, we train Energy-Based Transformers (EBTs) -- a new class of Energy-Based Models (EBMs) -- to assign an energy value to every input and candidate-prediction pair, enabling predictions through gradient descent-based energy minimization until convergence. Across both discrete (text) and continuous (visual) modalities, we find EBTs scale faster than the dominant Transformer++ approach during training, achieving an up to 35% higher scaling rate with respect to data, batch size, parameters, FLOPs, and depth. During inference, EBTs improve performance with System 2 Thinking by 29% more than the Transformer++ on language tasks, and EBTs outperform Diffusion Transformers on image denoising while using fewer forward passes. Further, we find that EBTs achieve better results than existing models on most downstream tasks given the same or worse pretraining performance, suggesting that EBTs generalize better than existing approaches. Consequently, EBTs are a promising new paradigm for scaling both the learning and thinking capabilities of models.
Recent advancements in multi-scale architectures have demonstrated exceptional performance in image denoising tasks. However, existing architectures mainly depends on a fixed single-input single-output Unet architecture, ignoring the multi-scale representations of pixel level. In addition, previous methods treat the frequency domain uniformly, ignoring the different characteristics of high-frequency and low-frequency noise. In this paper, we propose a novel multi-scale adaptive dual-domain network (MADNet) for image denoising. We use image pyramid inputs to restore noise-free results from low-resolution images. In order to realize the interaction of high-frequency and low-frequency information, we design an adaptive spatial-frequency learning unit (ASFU), where a learnable mask is used to separate the information into high-frequency and low-frequency components. In the skip connections, we design a global feature fusion block to enhance the features at different scales. Extensive experiments on both synthetic and real noisy image datasets verify the effectiveness of MADNet compared with current state-of-the-art denoising approaches.
Endoscopes featuring a miniaturized design have significantly enhanced operational flexibility, portability, and diagnostic capability while substantially reducing the invasiveness of medical procedures. Recently, single-use endoscopes equipped with an ultra-compact analogue image sensor measuring less than 1mm x 1mm bring revolutionary advancements to medical diagnosis. They reduce the structural redundancy and large capital expenditures associated with reusable devices, eliminate the risk of patient infections caused by inadequate disinfection, and alleviate patient suffering. However, the limited photosensitive area results in reduced photon capture per pixel, requiring higher photon sensitivity settings to maintain adequate brightness. In high-contrast medical imaging scenarios, the small-sized sensor exhibits a constrained dynamic range, making it difficult to simultaneously capture details in both highlights and shadows, and additional localized digital gain is required to compensate. Moreover, the simplified circuit design and analog signal transmission introduce additional noise sources. These factors collectively contribute to significant noise issues in processed endoscopic images. In this work, we developed a comprehensive noise model for analog image sensors in medical endoscopes, addressing three primary noise types: fixed-pattern noise, periodic banding noise, and mixed Poisson-Gaussian noise. Building on this analysis, we propose a hybrid denoising system that synergistically combines traditional image processing algorithms with advanced learning-based techniques for captured raw frames from sensors. Experiments demonstrate that our approach effectively reduces image noise without fine detail loss or color distortion, while achieving real-time performance on FPGA platforms and an average PSNR improvement from 21.16 to 33.05 on our test dataset.
Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an $\ell_2$-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable as a Moreau envelope. The crux is the selection of a parameter $a$ characterizing the graph Huber function that ensures overall objective convexity; we efficiently compute $a$ via an adaptation of Gershgorin Circle Theorem (GCT). To minimize the convex objective, we design a linear-time algorithm based on Alternating Direction Method of Multipliers (ADMM) and unroll it into a lightweight feed-forward network for data-driven parameter learning. Experiments show that our method outperforms unrolled GTV and other representative image denoising schemes, while employing far fewer network parameters.
The self-attention mechanism, a cornerstone of Transformer-based state-of-the-art deep learning architectures, is largely heuristic-driven and fundamentally challenging to interpret. Establishing a robust theoretical foundation to explain its remarkable success and limitations has therefore become an increasingly prominent focus in recent research. Some notable directions have explored understanding self-attention through the lens of image denoising and nonparametric regression. While promising, existing frameworks still lack a deeper mechanistic interpretation of various architectural components that enhance self-attention, both in its original formulation and subsequent variants. In this work, we aim to advance this understanding by developing a unifying image processing framework, capable of explaining not only the self-attention computation itself but also the role of components such as positional encoding and residual connections, including numerous later variants. We also pinpoint potential distinctions between the two concepts building upon our framework, and make effort to close this gap. We introduce two independent architectural modifications within transformers. While our primary objective is interpretability, we empirically observe that image processing-inspired modifications can also lead to notably improved accuracy and robustness against data contamination and adversaries across language and vision tasks as well as better long sequence understanding.
The rapid advancement of photography has created a growing demand for a practical blind raw image denoising method. Recently, learning-based methods have become mainstream due to their excellent performance. However, most existing learning-based methods suffer from camera-specific data dependency, resulting in performance drops when applied to data from unknown cameras. To address this challenge, we introduce a novel blind raw image denoising method named YOND, which represents You Only Need a Denoiser. Trained solely on synthetic data, YOND can generalize robustly to noisy raw images captured by diverse unknown cameras. Specifically, we propose three key modules to guarantee the practicality of YOND: coarse-to-fine noise estimation (CNE), expectation-matched variance-stabilizing transform (EM-VST), and SNR-guided denoiser (SNR-Net). Firstly, we propose CNE to identify the camera noise characteristic, refining the estimated noise parameters based on the coarse denoised image. Secondly, we propose EM-VST to eliminate camera-specific data dependency, correcting the bias expectation of VST according to the noisy image. Finally, we propose SNR-Net to offer controllable raw image denoising, supporting adaptive adjustments and manual fine-tuning. Extensive experiments on unknown cameras, along with flexible solutions for challenging cases, demonstrate the superior practicality of our method. The source code will be publicly available at the \href{https://fenghansen.github.io/publication/YOND}{project homepage}.
Low-light image denoising and enhancement are challenging, especially when traditional noise assumptions, such as Gaussian noise, do not hold in majority. In many real-world scenarios, such as low-light imaging, noise is signal-dependent and is better represented as Poisson noise. In this work, we address the problem of denoising images degraded by Poisson noise under extreme low-light conditions. We introduce a light-weight deep learning-based method that integrates Retinex based decomposition with Poisson denoising into a unified encoder-decoder network. The model simultaneously enhances illumination and suppresses noise by incorporating a Poisson denoising loss to address signal-dependent noise. Without prior requirement for reflectance and illumination, the network learns an effective decomposition process while ensuring consistent reflectance and smooth illumination without causing any form of color distortion. The experimental results demonstrate the effectiveness and practicality of the proposed low-light illumination enhancement method. Our method significantly improves visibility and brightness in low-light conditions, while preserving image structure and color constancy under ambient illumination.
We introduce a novel weighted convolution operator that enhances traditional convolutional neural networks (CNNs) by integrating a spatial density function into the convolution operator. This extension enables the network to differentially weight neighbouring pixels based on their relative position to the reference pixel, improving spatial characterisation and feature extraction. The proposed operator maintains the same number of trainable parameters and is fully compatible with existing CNN architectures. Although developed for 2D image data, the framework is generalisable to signals on regular grids of arbitrary dimensions, such as 3D volumetric data or 1D time series. We propose an efficient implementation of the weighted convolution by pre-computing the density function and achieving execution times comparable to standard convolution layers. We evaluate our method on two deep learning tasks: image classification using the CIFAR-100 dataset [KH+09] and image denoising using the DIV2K dataset [AT17]. Experimental results with state-of-the-art classification (e.g., VGG [SZ15], ResNet [HZRS16]) and denoising (e.g., DnCNN [ZZC+17], NAFNet [CCZS22]) methods show that the weighted convolution improves performance with respect to standard convolution across different quantitative metrics. For example, VGG achieves an accuracy of 66.94% with weighted convolution versus 56.89% with standard convolution on the classification problem, while DnCNN improves the PSNR value from 20.17 to 22.63 on the denoising problem. All models were trained on the CINECA Leonardo cluster to reduce the execution time and improve the tuning of the density function values. The PyTorch implementation of the weighted convolution is publicly available at: https://github.com/cammarasana123/weightedConvolution2.0.
The paper introduces the weighted convolution, a novel approach to the convolution for signals defined on regular grids (e.g., 2D images) through the application of an optimal density function to scale the contribution of neighbouring pixels based on their distance from the central pixel. This choice differs from the traditional uniform convolution, which treats all neighbouring pixels equally. Our weighted convolution can be applied to convolutional neural network problems to improve the approximation accuracy. Given a convolutional network, we define a framework to compute the optimal density function through a minimisation model. The framework separates the optimisation of the convolutional kernel weights (using stochastic gradient descent) from the optimisation of the density function (using DIRECT-L). Experimental results on a learning model for an image-to-image task (e.g., image denoising) show that the weighted convolution significantly reduces the loss (up to 53% improvement) and increases the test accuracy compared to standard convolution. While this method increases execution time by 11%, it is robust across several hyperparameters of the learning model. Future work will apply the weighted convolution to real-case 2D and 3D image convolutional learning problems.
Remote sensing image (RSI) denoising is an important topic in the field of remote sensing. Despite the impressive denoising performance of RSI denoising methods, most current deep learning-based approaches function as black boxes and lack integration with physical information models, leading to limited interpretability. Additionally, many methods may struggle with insufficient attention to non-local self-similarity in RSI and require tedious tuning of regularization parameters to achieve optimal performance, particularly in conventional iterative optimization approaches. In this paper, we first propose a novel RSI denoising method named sparse tensor-aided representation network (STAR-Net), which leverages a low-rank prior to effectively capture the non-local self-similarity within RSI. Furthermore, we extend STAR-Net to a sparse variant called STAR-Net-S to deal with the interference caused by non-Gaussian noise in original RSI for the purpose of improving robustness. Different from conventional iterative optimization, we develop an alternating direction method of multipliers (ADMM)-guided deep unrolling network, in which all regularization parameters can be automatically learned, thus inheriting the advantages of both model-based and deep learning-based approaches and successfully addressing the above-mentioned shortcomings. Comprehensive experiments on synthetic and real-world datasets demonstrate that STAR-Net and STAR-Net-S outperform state-of-the-art RSI denoising methods.
All techniques for denoising involve a notion of a true (noise-free) image, and a hypothesis space. The hypothesis space may reconstruct the image directly as a grayscale valued function, or indirectly by its Fourier or wavelet spectrum. Most common techniques estimate the true image as a projection to some subspace. We propose an interpretation of a noisy image as a collection of samples drawn from a certain probability space. Within this interpretation, projection based approaches are not guaranteed to be unbiased and convergent. We present a data-driven denoising method in which the true image is recovered as a conditional expectation. Although the probability space is unknown apriori, integrals on this space can be estimated by kernel integral operators. The true image is reformulated as the least squares solution to a linear equation in a reproducing kernel Hilbert space (RKHS), and involving various kernel integral operators as linear transforms. Assuming the true image to be a continuous function on a compact planar domain, the technique is shown to be convergent as the number of pixels goes to infinity. We also show that for a picture with finite number of pixels, the convergence result can be used to choose the various parameters for an optimum denoising result.
Self-supervised image denoising methods have garnered significant research attention in recent years, for this kind of method reduces the requirement of large training datasets. Compared to supervised methods, self-supervised methods rely more on the prior embedded in deep networks themselves. As a result, most of the self-supervised methods are designed with Convolution Neural Networks (CNNs) architectures, which well capture one of the most important image prior, translation equivariant prior. Inspired by the great success achieved by the introduction of translational equivariance, in this paper, we explore the way to further incorporate another important image prior. Specifically, we first apply high-accuracy rotation equivariant convolution to self-supervised image denoising. Through rigorous theoretical analysis, we have proved that simply replacing all the convolution layers with rotation equivariant convolution layers would modify the network into its rotation equivariant version. To the best of our knowledge, this is the first time that rotation equivariant image prior is introduced to self-supervised image denoising at the network architecture level with a comprehensive theoretical analysis of equivariance errors, which offers a new perspective to the field of self-supervised image denoising. Moreover, to further improve the performance, we design a new mask mechanism to fusion the output of rotation equivariant network and vanilla CNN-based network, and construct an adaptive rotation equivariant framework. Through extensive experiments on three typical methods, we have demonstrated the effectiveness of the proposed method.
All-in-one image restoration aims to recover clear images from various degradation types and levels with a unified model. Nonetheless, the significant variations among degradation types present challenges for training a universal model, often resulting in task interference, where the gradient update directions of different tasks may diverge due to shared parameters. To address this issue, motivated by the routing strategy, we propose DFPIR, a novel all-in-one image restorer that introduces Degradation-aware Feature Perturbations(DFP) to adjust the feature space to align with the unified parameter space. In this paper, the feature perturbations primarily include channel-wise perturbations and attention-wise perturbations. Specifically, channel-wise perturbations are implemented by shuffling the channels in high-dimensional space guided by degradation types, while attention-wise perturbations are achieved through selective masking in the attention space. To achieve these goals, we propose a Degradation-Guided Perturbation Block (DGPB) to implement these two functions, positioned between the encoding and decoding stages of the encoder-decoder architecture. Extensive experimental results demonstrate that DFPIR achieves state-of-the-art performance on several all-in-one image restoration tasks including image denoising, image dehazing, image deraining, motion deblurring, and low-light image enhancement. Our codes are available at https://github.com/TxpHome/DFPIR.
In imaging inverse problems, we would like to know how close the recovered image is to the true image in terms of full-reference image quality (FRIQ) metrics like PSNR, SSIM, LPIPS, etc. This is especially important in safety-critical applications like medical imaging, where knowing that, say, the SSIM was poor could potentially avoid a costly misdiagnosis. But since we don't know the true image, computing FRIQ is non-trivial. In this work, we combine conformal prediction with approximate posterior sampling to construct bounds on FRIQ that are guaranteed to hold up to a user-specified error probability. We demonstrate our approach on image denoising and accelerated magnetic resonance imaging (MRI) problems. Code is available at https://github.com/jwen307/quality_uq.
Electrocardiogram (ECG) signals are frequently corrupted by noise, such as baseline wander (BW), muscle artifacts (MA), and electrode motion (EM), which significantly degrade their diagnostic utility. To address this issue, we propose ECGDeDRDNet, a deep learning-based ECG Denoising framework leveraging a Double Recurrent Dense Network architecture. In contrast to traditional approaches, we introduce a double recurrent scheme to enhance information reuse from both ECG waveforms and the estimated clean image. For ECG waveform processing, our basic model employs LSTM layers cascaded with DenseNet blocks. The estimated clean ECG image, obtained by subtracting predicted noise components from the noisy input, is iteratively fed back into the model. This dual recurrent architecture enables comprehensive utilization of both temporal waveform features and spatial image details, leading to more effective noise suppression. Experimental results on the MIT-BIH dataset demonstrate that our method achieves superior performance compared to conventional image denoising methods in terms of PSNR and SSIM while also surpassing classical ECG denoising techniques in both SNR and RMSE.
Breast cancer is the most frequently diagnosed human cancer in the United States at present. Early detection is crucial for its successful treatment. X-ray mammography and digital breast tomosynthesis are currently the main methods for breast cancer screening. However, both have known limitations in terms of their sensitivity and specificity to breast cancers, while also frequently causing patient discomfort due to the requirement for breast compression. Breast computed tomography is a promising alternative, however, to obtain high-quality images, the X-ray dose needs to be sufficiently high. As the breast is highly radiosensitive, dose reduction is particularly important. Phase-contrast computed tomography (PCT) has been shown to produce higher-quality images at lower doses and has no need for breast compression. It is demonstrated in the present study that, when imaging full fresh mastectomy samples with PCT, deep learning-based image denoising can further reduce the radiation dose by a factor of 16 or more, without any loss of image quality. The image quality has been assessed both in terms of objective metrics, such as spatial resolution and contrast-to-noise ratio, as well as in an observer study by experienced medical imaging specialists and radiologists. This work was carried out in preparation for live patient PCT breast cancer imaging, initially at specialized synchrotron facilities.
Echocardiography (echo), or cardiac ultrasound, is the most widely used imaging modality for cardiac form and function due to its relatively low cost, rapid acquisition time, and non-invasive nature. However, ultrasound acquisitions are often limited by artifacts and noise that hinder diagnostic interpretation in clinical settings. Existing methodologies for denoising echos consist solely of traditional filtering-based algorithms or deep learning methods developed on radio-frequency (RF) signals which prevents clinical applicability and scalability. To address these limitations, we introduce the first deep generative model capable of simulating ultrasound noise developed on B-mode data. Using this generative model, we develop a synthetic dataset of paired clean and noisy echo images to train a downstream model for real-world image denoising and demonstrate state-of-the-art performance in both internal and external experiments. In both held-out test sets, our method results in echo images with higher gCNR in comparison to noisy image counterparts and images derived from a comparable method which is consistent with provided visual comparisons. Our experiments showcase the potential of our method for future clinical use to improve the quality of echo acquisitions. To encourage further research into the field, we release our source code and model weights at https://github.com/echonet/image_quality.
Noise synthesis is a promising solution for addressing the data shortage problem in data-driven low-light RAW image denoising. However, accurate noise synthesis methods often necessitate labor-intensive calibration and profiling procedures during preparation, preventing them from landing to practice at scale. This work introduces a practically simple noise synthesis pipeline based on detailed analyses of noise properties and extensive justification of widespread techniques. Compared to other approaches, our proposed pipeline eliminates the cumbersome system gain calibration and signal-independent noise profiling steps, reducing the preparation time for noise synthesis from days to hours. Meanwhile, our method exhibits strong denoising performance, showing an up to 0.54dB PSNR improvement over the current state-of-the-art noise synthesis technique. Code is released at https://github.com/SonyResearch/raw_image_denoising
Purpose: This work proposes a novel self-supervised noise-adaptive image denoising framework, called Repetition to Repetition (Rep2Rep) learning, for low-field (<1T) MRI applications. Methods: Rep2Rep learning extends the Noise2Noise framework by training a neural network on two repeated MRI acquisitions, using one repetition as input and another as target, without requiring ground-truth data. It incorporates noise-adaptive training, enabling denoising generalization across varying noise levels and flexible inference with any number of repetitions. Performance was evaluated on both synthetic noisy brain MRI and 0.55T prostate MRI data, and compared against supervised learning and Monte Carlo Stein's Unbiased Risk Estimator (MC-SURE). Results: Rep2Rep learning outperforms MC-SURE on both synthetic and 0.55T MRI datasets. On synthetic brain data, it achieved denoising quality comparable to supervised learning and surpassed MC-SURE, particularly in preserving structural details and reducing residual noise. On the 0.55T prostate MRI dataset, a reader study showed radiologists preferred Rep2Rep-denoised 2-average images over 8-average noisy images. Rep2Rep demonstrated robustness to noise-level discrepancies between training and inference, supporting its practical implementation. Conclusion: Rep2Rep learning offers an effective self-supervised denoising for low-field MRI by leveraging routinely acquired multi-repetition data. Its noise-adaptivity enables generalization to different SNR regimes without clean reference images. This makes Rep2Rep learning a promising tool for improving image quality and scan efficiency in low-field MRI.