Separating linear coherent noise, such as ground roll from reflections, remains a key challenge in seismic processing. By adapting the redundant lifting scheme (RLS), a wavelet transform method, to seismic data, we have determined how the wavelet domain can be used to suppress coherent and random noise. The RLS operates on a trace-by-trace basis decomposing each time series into wavelet-coefficient (WC) time series and consequently a single gather (in a shot, receiver, or common depth point domain) into a series of WC subgathers (SGs). The decomposition changes the relative magnitude of WCs of various events (reflection, head wave, ground roll, etc.) from one SG to another without affecting their moveout. In SG(s) in which the WCs of undesired events were significantly stronger than the desired events, the WCs can be surgically muted. Selective muting in carefully chosen SGs attenuates undesired events while having minimal effects on frequency spectra of the desired events. In addition, random noise can be suppressed in the individual SGs by designing a local thresholding mechanism (we have used modified Otsu thresholding) in combination with adaptive Wiener filtering. We have developed this approach of suppressing coherent and random noise in a step-by-step manner first using a synthetic shot gather, followed by demonstration on two real gathers. Our RLS-based denoising method has minimal effects on the lower end of signal frequency spectra, and it could be a valuable tool in a processor’s toolbox when data preconditioning for advanced processing such as waveform inversion, which benefits from low frequencies, is desired.
Detection of red lesions in color retinal images is a critical step to prevent the development of vision loss and blindness associated with diabetic retinopathy (DR). Microaneurysms (MAs) are the most frequently observed and are usually the first lesions to appear as a consequence of DR. Therefore, their detection is necessary for mass screening of DR. However, detecting these lesions is a challenging task because of the low image contrast, and the wide variation of imaging conditions. Recently, the emergence of computer-aided diagnosis systems offers promising approaches to detect these lesions for diagnostic purposes. In this paper we focus on developing unsupervised and supervised techniques to cope intelligently with the MAs detection problem. In the first step, the retinal images are preprocessed to remove background variation in order to achieve a high level of accuracy in the detection. In the main processing step, important landmarks such as the optic nerve head and retinal vessels are detected and masked using the Radon transform (RT) and multi-overlapping windows. Finally, the MAs are detected and numbered by using a combination of RT and a supervised support vector machine classifier. The method was tested on three publicly available datasets and a local database comprising a total of 749 images. Detection performance was evaluated using sensitivity, specificity, and FROC analysis. From the image analysis viewpoint, DR was detected with a sensitivity of 100% and a specificity of 93% on average across all of these databases. Moreover, from lesion-based analysis the proposed approach detected the MAs with sensitivity of 95.7% with an average of 7 false positives per image. These results compare favourably with the best of the published results to date.
Denoising becomes a non-trivial task when noise and signal overlap in multiple domains such as time, frequency, and velocity. Fortunately, signal and noise waveforms in general tend to remain morphologically different. This paper shows how morphological differences can be used to separate body-wave signals from other waveforms such as ground roll and cultural noise. The key was finding a wavelet that was a close approximation of the true source signature (SS) and remained uncontaminated by the Greens function in any significant manner. An inverse filter designed using such a wavelet selectively compressed the body waves which was then extracted using median and low-pass filters. The overall phenomenon is explained with a synthetic example. The idea is also tested on a land dataset that was generated using a large weight drop source where a wavelet recorded ∼3 m from the source location fulfilled the criteria set in the proposed method. Results suggest that the incremental effort of recording an extra trace close to the source location during acquisition may provide previously unavailable denoising opportunities during processing although the trace itself may be redundant for imaging.
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