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Register a new userA simple denoising algorithm using wavelet transform
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Manojit Roy
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Submission withdrawn because the authors erroneously submitted a revised version as a new submission, see nlin.CD/0002028.
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We propose a 2D generalization to the $M$-band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (textit{i}) the construction of the dual basis and (textit{ii}) the resulting directional analysis. We also revisit the necessary pre-processing stage in the $M$-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed $M$-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various $M$-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.
Recently, multidimensional data is produced in various domains; because a large volume of this data is often used in complex analytical tasks, it must be stored compactly and able to respond quickly to queries. Existing compression schemes well reduce the data storage; however, they might increase overall computational costs while performing queries. Effectively querying compressed data requires a compression scheme carefully designed for the tasks. This study presents a novel compression scheme, SEACOW, for storing and querying multidimensional array data. The scheme is based on wavelet transform and utilizes a hierarchical relationship between sub-arrays in the transformed data to compress the array. A result of the compression embeds a synopsis, improving query processing performance while acting as an index. To perform experiments, we implemented an array database, SEACOW storage, and evaluated query processing performance on real data sets. Our experiments show that 1) SEACOW provides a high compression ratio comparable to existing compression schemes and 2) the synopsis improves analytical query processing performance.
Multi-spectral satellite imaging sensors acquire various spectral band images such as red (R), green (G), blue (B), near-infrared (N), etc. Thanks to the unique spectroscopic property of each spectral band with respective to the objects on the ground, multi-spectral satellite imagery can be used for various geological survey applications. Unfortunately, image artifacts from imaging sensor noises often affect the quality of scenes and have negative impacts on the applications of satellite imagery. Recently, deep learning approaches have been extensively explored for the removal of noises in satellite imagery. Most deep learning denoising methods, however, follow a supervised learning scheme, which requires matched noisy image and clean image pairs that are difficult to collect in real situations. In this paper, we propose a novel unsupervised multispectral denoising method for satellite imagery using wavelet subband cycle-consistent adversarial network (WavCycleGAN). The proposed method is based on unsupervised learning scheme using adversarial loss and cycle-consistency loss to overcome the lack of paired data. Moreover, in contrast to the standard image domain cycleGAN, we introduce a wavelet subband domain learning scheme for effective denoising without sacrificing high frequency components such as edges and detail information. Experimental results for the removal of vertical stripe and wave noises in satellite imaging sensors demonstrate that the proposed method effectively removes noises and preserves important high frequency features of satellite images.
Recognizing fonts has become an important task in document analysis, due to the increasing number of available digital documents in different fonts and emphases. A generic font-recognition system independent of language, script and content is desirable for processing various types of documents. At the same time, categorizing calligraphy styles in handwritten manuscripts is important for palaeographic analysis, but has not been studied sufficiently in the literature. We address the font-recognition problem as analysis and categorization of textures. We extract features using complex wavelet transform and use support vector machines for classification. Extensive experimental evaluations on different datasets in four languages and comparisons with state-of-the-art studies show that our proposed method achieves higher recognition accuracy while being computationally simpler. Furthermore, on a new dataset generated from Ottoman manuscripts, we show that the proposed method can also be used for categorizing Ottoman calligraphy with high accuracy.
The Cosmic Dawn and Epoch of Reionisation, during which collapsed structures produce the first ionising photons and proceed to reionise the intergalactic medium, span a large range in redshift (z~30-6) and time (t_{age} ~ 0.1-1.0~Gyr). Exploration of these epochs using the redshifted 21~cm emission line from neutral hydrogen is currently limited to statistical detection and estimation metrics (e.g., the power spectrum) due to the weakness of the signal. Brightness temperature fluctuations in the line-of-sight (LOS) dimension are probed by observing the emission line at different frequencies, and their structure is used as a primary discriminant between the cosmological signal and contaminating foreground extragalactic and Galactic continuum emission. Evolution of the signal over the observing bandwidth leads to the `line cone effect whereby the HI structures at the start and end of the observing band are not statistically consistent, yielding a biased estimate of the signal power, and potential reduction in signal detectability. We implement a wavelet transform to wide bandwidth radio interferometry experiments to probe the local statistical properties of the signal. We show that use of the wavelet transform yields estimates with improved estimation performance, compared with the standard Fourier Transform over a fixed bandwidth. With the suite of current and future large bandwidth reionisation experiments, such as with the 300~MHz instantaneous bandwidth of the Square Kilometre Array, a transform that retains local information will be important.
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