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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
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The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
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Alliance: All-in-One Spectral-Spatial-Frequency Awareness Foundation Model.

Boyu Zhao, Wei Li, Junjie Wang

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |December 3, 2025
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces the All-in-One Spectral-Spatial-Frequency Awareness Foundation Model (Alliance) for remote sensing. Alliance effectively integrates spectral, spatial, and frequency information, significantly improving foundation model performance on diverse tasks.

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    Area of Science:

    • Remote Sensing
    • Computer Vision
    • Signal Processing

    Background:

    • Foundation models (FMs) in remote sensing excel with spatial and spectral data but underutilize frequency domain information.
    • Existing FMs struggle to bridge the semantic gap between frequency characteristics and original image content, hindering downstream task performance.

    Purpose of the Study:

    • To develop a novel foundation model, Alliance, that comprehensively integrates spectral, spatial, and frequency information for enhanced remote sensing analysis.
    • To address the limitations of current FMs in capturing hidden features within the frequency domain and maintaining multi-domain coherence.

    Main Methods:

    • Proposed the All-in-One Spectral-Spatial-Frequency Awareness Foundation Model (Alliance) framework.
    • Introduced a progressive frequency decoding mechanism mimicking human visual cognition to minimize multi-domain information gaps.
    • Developed a triple-domain fusion attention module for integrated processing of amplitude, phase, and spectral-spatial relationships.
    • Implemented frequency embedding with specialized token initialization for fine-grained frequency band modeling.

    Main Results:

    • Alliance demonstrated superior performance across six downstream remote sensing tasks.
    • The progressive frequency decoding effectively extracts subtle image patterns difficult to observe in raw pixel values.
    • The triple-domain fusion attention and frequency embedding enabled comprehensive feature integration and fine-grained modeling.

    Conclusions:

    • Alliance represents a significant advancement in foundation models for remote sensing by effectively leveraging the frequency domain.
    • The proposed methods successfully bridge the semantic gap between different data domains, leading to improved generalizability and performance.
    • The Yellow River dataset provides a robust benchmark for evaluating FM capabilities in challenging cross-domain remote sensing scenarios.