Neural fields or implicit neural representations (INRs) have attracted significant attention in machine learning and signal processing due to their efficient continuous representation of images and 3D volumes. In this work, we build on INRs and introduce a coordinate-based local processing framework for solving imaging inverse problems, termed LoFi (Local Field). Unlike conventional methods for image reconstruction, LoFi processes local information at each coordinate \textit{separately} by multi-layer perceptrons (MLPs), recovering the object at that specific coordinate. Similar to INRs, LoFi can recover images at any continuous coordinate, enabling image reconstruction at multiple resolutions. With comparable or better performance than standard CNNs for image reconstruction, LoFi achieves excellent generalization to out-of-distribution data and memory usage almost independent of image resolution. Remarkably, training on $1024 \times 1024$ images requires just 3GB of memory -- over 20 times less than the memory typically needed by standard CNNs. Additionally, LoFi's local design allows it to train on extremely small datasets with less than 10 samples, without overfitting or the need for regularization or early stopping. Finally, we use LoFi as a denoising prior in a plug-and-play framework for solving general inverse problems to benefit from its continuous image representation and strong generalization. Although trained on low-resolution images, LoFi can be used as a low-dimensional prior to solve inverse problems at any resolution. We validate our framework across a variety of imaging modalities, from low-dose computed tomography to radio interferometric imaging.

翻译：神经场或隐式神经表示（INRs）因其对图像和三维体积的高效连续表示，在机器学习和信号处理领域引起了广泛关注。本研究基于INRs，提出了一种基于坐标的局部处理框架以解决成像逆问题，称为LoFi（局部场）。与传统的图像重建方法不同，LoFi通过多层感知机（MLPs）在每个坐标上独立处理局部信息，从而恢复该特定坐标处的物体。与INRs类似，LoFi能够在任意连续坐标处恢复图像，实现多分辨率图像重建。LoFi在图像重建任务中取得了与标准CNN相当或更优的性能，同时展现出对分布外数据的出色泛化能力，且内存使用量几乎与图像分辨率无关。值得注意的是，在$1024 \times 1024$图像上进行训练仅需3GB内存——比标准CNN通常所需内存少20倍以上。此外，LoFi的局部设计使其能够在少于10个样本的极小数据集上进行训练，而不会过拟合，也无需正则化或早停策略。最后，我们将LoFi作为去噪先验应用于即插即用框架中，以解决一般逆问题，从而受益于其连续的图像表示和强大的泛化能力。尽管在低分辨率图像上训练，LoFi仍可作为低维先验用于解决任意分辨率的逆问题。我们在多种成像模态上验证了该框架的有效性，涵盖从低剂量计算机断层扫描到射电干涉成像等应用。