We introduce a new method for estimating the Ideal Time-Frequency Representation (ITFR) of complex nonstationary signals. The Reconstructive Ideal Fractional Transform (RIFT) computes a constellation of Continuous Fractional Wavelet Transforms (CFWTs) aligned to different local time-frequency curvatures. This constellation is combined into a single optimised time-frequency energy representation via a localised entropy-based sparsity measure, designed to resolve auto-terms and attenuate cross-terms. Finally, a positivity-constrained Lucy-Richardson deconvolution with total-variation regularisation is applied to estimate the ITFR, achieving auto-term resolution comparable to that of the Wigner-Ville Distribution (WVD), yielding the high-resolution RIFT representation. The required Cohen's class convolutional kernels are fully derived in the paper for the chosen CFWT constellations. Additionally, the optimisation yields an Instantaneous Phase Direction (IPD) field, which allows the localised curvature in speech or music extracts to be visualised and utilised within a Kalman tracking scheme, enabling the extraction of signal component trajectories and the construction of the Spline-RIFT variant. Evaluation on synthetic and real-world signals demonstrates the algorithm's ability to effectively suppress cross-terms and achieve superior time-frequency precision relative to competing methods. This advance holds significant potential for a wide range of applications requiring high-resolution cross-term-free time-frequency analysis.

翻译：我们提出了一种估计复杂非平稳信号理想时频表示（ITFR）的新方法。重构性理想分数阶变换（RIFT）通过计算一组连续分数阶小波变换（CFWT）的星座图，使其对齐于不同的局部时频曲率。该星座图通过一种基于局部熵的稀疏性度量被融合为单一优化的时频能量表示，该度量旨在解析自项并抑制交叉项。最终，采用带全变差正则化的非负约束Lucy-Richardson反卷积来估计ITFR，实现了与维格纳-维尔分布（WVD）相当的自项分辨率，从而获得高分辨率的RIFT表示。本文完整推导了所选CFWT星座图所需的Cohen类卷积核。此外，该优化过程还生成了瞬时相位方向（IPD）场，使得语音或音乐片段中的局部曲率得以可视化，并可在卡尔曼跟踪框架中加以利用，从而提取信号分量轨迹并构建Spline-RIFT变体。在合成信号和真实信号上的评估表明，该算法能够有效抑制交叉项，并在时频精度方面优于竞品方法。这一进展在需要高分辨率无交叉项时频分析的广泛应用中具有重要潜力。