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Suitable extraction of an object’s wave field in an off-axis digital holographic array is the core for any numerical reconstruction process. In this manuscript, we propose an algorithm that reduces the number of pixels needed for an object’s wave field trimming, reducing notably its processing time without significant changes in the quality of the reconstructed image. Our method generates an extraction window containing a complete object’s wave field. The energy that the generated extraction window must contain is analyzed, defined, and used as a reference value. Our proposal reduces significantly the number of operations and execution time for holographic reconstruction.

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An efficient computation of a composite length discrete Fourier transform (DFT), as well as a fast Fourier transform (FFT) of both time and space data sequences in uncertain (non-sparse or sparse) computational scenarios, requires specific processing algorithms. Traditional algorithms typically employ some pruning methods without any commutations, which prevents them from attaining the potential computational efficiency. In this paper, we propose an alternative unified approach with automatic commutations between three computational modalities aimed at efficient computations of the pruned DFTs adapted for variable composite lengths of the non-sparse input-output data. The first modality is an implementation of the direct computation of a composite length DFT, the second one employs the second-order recursive filtering method, and the third one performs the new pruned decomposed transform. The pruned decomposed transform algorithm performs the decimation in time or space (DIT) data acquisition domain and, then, decimation in frequency (DIF). The unified combination of these three algorithms is addressed as the DFT COMM technique. Based on the treatment of the combinational-type hypotheses testing optimization problem of preferable allocations between all feasible commuting-pruning modalities, we have found the global optimal solution to the pruning problem that always requires a fewer or, at most, the same number of arithmetic operations than other feasible modalities. The DFT COMM method outperforms the existing competing pruning techniques in the sense of attainable savings in the number of required arithmetic operations. It requires fewer or at most the same number of arithmetic operations for its execution than any other of the competing pruning methods reported in the literature. Finally, we provide the comparison of the DFT COMM with the recently developed sparse fast Fourier transform (SFFT) algorithmic family. We feature that, in the sensing scenarios with sparse/non-sparse data Fourier spectrum, the DFT COMM technique manifests robustness against such model uncertainties in the sense of insensitivity for sparsity/non-sparsity restrictions and the variability of the operating parameters.