Simultaneous denoising and resolution enhancement of seismic data based on elastic convolution dictionary learning

Enhancing seismic resolution is a key component in seismic data processing, which plays a valuable role in raising the prospecting accuracy of oil reservoirs. However, in noisy situations, existing resolution enhancement methods are difficult to yield satisfactory processing outcomes for reservoir characterization. To solve this problem, we develop a new approach for simultaneous denoising and resolution enhancement of seismic data based on convolution dictionary learning. First, an elastic convolution dictionary learning algorithm is presented to efficiently learn a convolution dictionary with stronger representation capability from the noisy data to be processed. Specifically, the algorithm introduces the elastic L1/2 norm as a sparsity constraint and employs a steepest gradient descent strategy to efficiently solve the frequency-domain linear system with substantial computational cost in a half-quadratic splitting framework. Then, based on the learned convolution dictionary, a weighted convolutional sparse representation paradigm is designed to encode the noisy data to acquire an optimal sparse approximation of the effective signal. Subsequently, a high-resolution dictionary with a broadband spectrum is constructed by the proposed parameter scaling strategy and matched filtering technique on the basis of atomic spectrum modeling. Finally, the optimal sparse approximation of the effective signal and the constructed high-resolution dictionary are used for data reconstruction to obtain the seismic signal with high resolution and high signal-to-noise ratio. Synthetic and field dataset examples are executed to check the effectiveness and reliability of the developed method. The results indicate that this method has a more competitive performance in seismic applications compared with the conventional deconvolution and spectral whitening methods.

Visibility and Resolution Enhancement of Fourth-Order Ghost Interference with Thermal Light

A scheme for fourth-order double-slit ghost interference with a pseudo-thermal light source is proposed. It is shown that not only can the visibility be dramatically enhanced compared to the third-order case, but also higher resolution is demonstrated if we scan two of three reference detectors in opposite directions with the same speed, meanwhile another two in identical directions where the speed of one reference detector is twice the other. The results show that the visibility and resolution improvement of the fourth-order ghost interference fringe can be applied to the Nth-order ghost imaging.

Resolution enhancement of digital holographic microscopy via synthetic aperture:a review

Digital holographic microscopy(DHM),which combines digital holography with optical microscopy,is a wide field,minimally invasive quantitative phase microscopy(QPM)approach for measuring the 3D shape or the inner structure of transparent and translucent samples.However,limited by diffraction,the spatial resolution of conventional DHM is relatively low and incompatible with a wide field of view(FOV)owing to the spatial bandwidth product(SBP)limit of the imaging systems.During the past decades,many efforts have been made to enhance the spatial resolution of DHM while preserving a large FOV by trading with unused degrees of freedom.Illumination modulation techniques,such as oblique illumination,structured illumination,and speckle illumination,can enhance the resolution by adding more high-frequency information to the recording system.Resolution enhancement is also achieved by extrapolation of a hologram or by synthesizing a larger hologram by scanning the sample,the camera,or inserting a diffraction grating between the sample and the camera.For on-chip DHM,spatial resolution is achieved using pixel super-resolution techniques.In this paper,we review various resolution enhancement approaches in DHM and discuss the advantages and disadvantages of these approaches.It is our hope that this review will contribute to advancements in DHM and its practical applications in many fields.

Resolution enhancement of optical scanning holography with a spiral modulated point spread function

In optical scanning holography, one pupil produces a spherical wave and another produces a plane wave. They interfere with each other and result in a fringe pattern for scanning a three-dimensional object. The resolution of the hologram reconstruction is affected by the point spread function(PSF) of the optical system. In this paper, we modulate the PSF by a spiral phase plate, which significantly enhances the lateral and depth resolution. We explain the theory for such resolution enhancement and show simulation results to verify the efficacy of the approach.

Resolution-enhanced single-pixel imaging using the Hadamard transform matrix

We propose a single-pixel imaging(SPI)method to achieve a higher-resolution image via the Hadamard transform matrix.Unlike traditional SPI schemes,this new method recovers images by correlating single-pixel signals with synchronized transformed patterns of Hadamard bases that are actually projected onto the digital micromirror device.Each transform pattern is obtained through the inverse Fourier transform of the pattern acquired by Gaussian filtering of each Hadamard basis in the frequency domain.The proposed scheme is based on a typical SPI experimental setup and does not add any hardware complexity,enabling the transformation of Hadamard matrices and image reconstruction through data processing alone.Therefore,this approach could be considered as an alternative option for achieving fast SPI in a diffraction-limited imaging system,without the need for additional hardware.

Time-resolution enhanced multi-path OTD measurement using an adaptive filter based incoherent OFDR

High accuracy and time resolution optical transfer delay(OTD)measurement is highly desired in many multi-path applications,such as optical true-time-delay-based array systems and distributed optical sensors.However,the time resolution is usually limited by the frequency range of the probe signal in frequency-multiplexed OTD measurement techniques.Here,we proposed a time-resolution enhanced OTD measurement method based on incoherent optical frequency domain reflectometry(I-OFDR),where an adaptive filter is designed to suppress the spectral leakage from other paths to break the resolution limitation.A weighted least square(WLS)cost function is first established,and then an iteration approach is used to minimize the cost function.Finally,the appropriate filter parameter is obtained according to the convergence results.In a proof-of-concept experiment,the time-domain response of two optical links with a length difference of 900 ps is successfully estimated by applying a probe signal with a bandwidth of 400 MHz.The time resolution is improved by 2.78times compared to the theoretical resolution limit of the inverse discrete Fourier transform(iDFT)algorithm.In addition,the OTD measurement error is below±0.8 ps.The proposed algorithm provides a novel way to improve the measurement resolution without applying a probe signal with a large bandwidth,avoiding measurement errors induced by the dispersion effect.

Phase-only hologram generation based on integral imaging and its enhancement in depth resolution

We introduce a phase-only hologram generation method based on an integral imaging, and propose an enhancement method in representable depth interval. The computational integral imaging reconstruction method is modified based on optical flow to obtain depth-slice images for the focused objects only. A phaseonly hologram for＇ multiple plane images is generated using the iterative Fresnel transform algorithm. In addition, a division method in hologram plane is proposed for enhancement in the representable minimum depth interval.