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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Pseudoinverse Decoding Process in Delay-Encoded Synthetic Transmit Aperture Imaging.

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    Delay-encoded synthetic transmit aperture (DE-STA) imaging offers a stable method for improving signal-to-noise ratio. Noise primarily impacts early signals, but image quality remains consistent between complete and truncated pseudoinverse methods.

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    Area of Science:

    • Medical Imaging
    • Ultrasound Technology
    • Signal Processing

    Background:

    • Synthetic Transmit Aperture (STA) imaging enhances image quality in ultrasound.
    • Improving the signal-to-noise ratio (SNR) of prebeamformed radio-frequency data is crucial for robust imaging.
    • Direct inversion of the coding matrix in DE-STA is ill-posed, especially in noisy conditions.

    Purpose of the Study:

    • To investigate the stability and performance of Delay-Encoded Synthetic Transmit Aperture (DE-STA) imaging under varying noise levels.
    • To analyze the effectiveness of pseudoinverse (PI) methods, specifically complete PI (CPI) and truncated PI (TPI), in DE-STA decoding.
    • To develop a more efficient decoding formula for DE-STA based on the coding matrix's singular value properties.

    Main Methods:

    • Application of Singular Value Decomposition (SVD) to the DE-STA coding matrix for pseudoinverse calculation.
    • Comparison of Complete Pseudoinverse (CPI) and Truncated Pseudoinverse (TPI) decoding strategies.
    • Numerical simulations and experimental validation of DE-STA performance with added noise.
    • Development and analysis of a novel decoding formula based on the conjugate transpose of the coding matrix.

    Main Results:

    • Singular value decomposition revealed a unique distribution in the coding matrix: all singular values are identical except for the first and last.
    • Both CPI and TPI methods demonstrated stable signal restoration, with noise predominantly affecting signals from the first transmit channel.
    • The difference in overall image quality between CPI and TPI was negligible, indicating the robustness of the DE-STA technique.
    • A new, efficient decoding formula based on the conjugate transpose of the coding matrix was proposed and compared computationally.

    Conclusions:

    • DE-STA is a stable and effective encoding/decoding technique for improving SNR in prebeamformed data.
    • The choice between CPI and TPI has minimal impact on final image quality, highlighting DE-STA's resilience to noise.
    • The proposed conjugate transpose-based decoding formula offers computational efficiency compared to direct inversion methods.