Method for the Reconstruction of One-Dimensional or Multidimensional Data

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This patent presents a mathematical method for reconstructing one-dimensional or multidimensional data (such as signals, images, or videos) that fit certain linear models. The invention improves upon existing techniques for removing noise, filling data gaps, and reducing artifacts in imperfect recorded data by using specifically-designed operations based on differential equations, structure tensors, and data characteristics. The method can be implemented in computer systems to provide higher-fidelity reconstructions than conventional approaches.

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• Denoising and reconstruction of medical images such as MRI, PET, or CT scans.
• Enhancement and artifact reduction in digital photographs or video sequences.
• Filling in missing data in scientific measurements, time series, or sensor arrays.
• Data restoration in spectroscopy, such as mass spectrometry or fluorescence spectra.
• Improving motion estimation and multi-camera data fusion in computer vision systems.
• Noise reduction in applied physics or engineering measurement data.

BenefitsContent extracted from patent full text and abstract with AI.

• Provides more accurate data reconstruction, reducing unwanted artifacts compared to standard diffusion and filtering techniques.
• Can handle both one-dimensional (e.g., signals, time series) and multidimensional data (e.g., images, video, volumetric sequences).
• Applicable to a wide range of data types and scientific domains, including medical imaging, physics, engineering, and computer vision.
• Capable of simultaneously denoising and filling missing or corrupted parts of the data.
• Does not rely solely on statistical or heuristic filtering but incorporates model-based approaches for improved results.
• Can be implemented in computerized processing systems for automated, reliable data enhancement.

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Patent Abstract

The invention relates to a method for reconstructing one-dimensional or multidimensional data corresponding to a linear model of the form D(I)T p = 0 (1), wherein I = recorded data, T = transposition, D = operator vector, and p = parameter vector. The inventive method is characterized in that the data is processed using the differential equation ?,I=D (M D (I)) (2), wherein D = operator vector that is obtained using point-by-point mirroring of the individual operators in D, M = tensor which is obtained by means of the extended structure tensor L, wherein Ly=B*(D1(I)Dj(I)), B being a smoothing operator.