Deep Neural Networks (DNNs) have been widely used for illumination estimation, which is time-consuming and requires sensor-specific data collection. Our proposed method uses a dual-mapping strategy and only requires a simple white point from a test sensor under a D65 condition. This allows us to derive a mapping matrix, enabling the reconstructions of image data and illuminants. In the second mapping phase, we transform the reconstructed image data into sparse features, which are then optimized with a lightweight multi-layer perceptron (MLP) model using the re-constructed illuminants as ground truths. This approach effectively reduces sensor discrepancies and delivers performance on par with leading cross-sensor methods. It only requires a small amount of memory (∼0.003 MB), and takes ∼1 hour training on an RTX3070Ti GPU. More importantly, the method can be implemented very fast, with ∼0.3 ms and ∼1 ms on a GPU or CPU respectively, and is not sensitive to the input image resolution. Therefore, it offers a practical solution to the great challenges of data recollection that is faced by the industry.