Directional information is an important and unique feature of multidimensional signals. As a result of a separable extension from 1D bases, the multidimensional wavelet transform has very limited directionality. Furth...
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Directional information is an important and unique feature of multidimensional signals. As a result of a separable extension from 1D bases, the multidimensional wavelet transform has very limited directionality. Furthermore, different directions are mixed in certain wavelet subbands. In this paper, we propose a new transform that fixes this frequency mixing problem by using a simple "add-on" to the wavelet transform. In the 2D case, it provides one lowpass subband and six directional highpass subbands at each scale. Just like the wavelet transform, the proposed transform is nonredundant, and can be easily extended to higher dimensions. Though nonseparable in essence, the proposed transform has an efficient implementation based on 1D operations only.
images are often corrupted as a result of various factors that can occur during acquisition and transmission processes. image denoising is aimed at removing or reducing noise, so that a good-quality image can be obtai...
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images are often corrupted as a result of various factors that can occur during acquisition and transmission processes. image denoising is aimed at removing or reducing noise, so that a good-quality image can be obtained for various applications. The paper presents a neural network based denoising method implemented in the wavelet transform domain. A noisy image is first wavelet transformed into four subbands, then a trained layered neural network is applied to each subband to generate noise-removed wavelet coefficients from their noisy ones. The denoised image is thereafter obtained through the inverse transform on the noise-removed wavelet coefficients. Simulation results demonstrate that this method is very efficient in removing noise. Compared with other methods performed in the wavelet domain, it requires no a priori knowledge about the noise and needs only one level of signal decomposition to obtain very good denoising results.
The wavelet transform is a very powerful tool for image coding for which the quality of the compression is depending on the choice of the filter banks associated to the wavelet. These filters can be characterized by t...
The wavelet transform is a very powerful tool for image coding for which the quality of the compression is depending on the choice of the filter banks associated to the wavelet. These filters can be characterized by two indices: a spatial index related to their significant support and a frequency index related to their aliasing. This work explores the connection between a quality criteria and these two indices for a given image family. Two useful applications are presented: in the first one a neural network allows us to deduce the best filter bank for a given image. In the second one a quality criterion for a new image is estimated knowing the filter bank.
Spherical maps occur in a range of applications for instance in geophysics or in astrophysics with the study of the cosmic microwave background (CMB) radiation field, where observations are over the whole sky. Analyzi...
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Spherical maps occur in a range of applications for instance in geophysics or in astrophysics with the study of the cosmic microwave background (CMB) radiation field, where observations are over the whole sky. Analyzing these images requires specific tools. This paper describes a new multiscale decomposition for data on the sphere, namely the curvelet transform on the sphere. The curvelet transform, in its first step, requires the use of an isotropic wavelet transform. Therefore, our new curvelet transform also includes a new wavelet transform on the sphere which has properties similar to those of the a trous isotropic wavelet transform.
Our aim is to detect events in digital signals. To make this detection the signals are considered to be piecewise stationary, with no a priori knowledge of the parameters of the hypotheses on the process state to be d...
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Our aim is to detect events in digital signals. To make this detection the signals are considered to be piecewise stationary, with no a priori knowledge of the parameters of the hypotheses on the process state to be detected. The detector is applied on the detail coefficients obtained after the application of the Mallat's fast decomposition algorithm without reconstruction of the detail signals. The association of wavelet transform and an algorithm of detection such as the cumulative sum applied on adaptive windows produces satisfactory results. The moments of detection obtained on each scale are shifted because the decimation and the convolution between a sequence of an approximation coefficients of a precedent level and the impulsion responses of low pass and high pass filters corresponding to the scaling and wavelet functions respectively. Equations of retiming to obtain the correct moment in original signal show important results.
This paper introduces the interlevel product (ILP) which is a transform based upon the dual-tree complex wavelet. Coefficients of the ILP have complex values whose magnitudes indicate the amplitude of multilevel featu...
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This paper introduces the interlevel product (ILP) which is a transform based upon the dual-tree complex wavelet. Coefficients of the ILP have complex values whose magnitudes indicate the amplitude of multilevel features, and whose phases indicate the nature of these features (e.g. ridges vs. edges). In particular, the phases of ILP coefficients are approximately invariant to small shifts in the original images. We accordingly introduce this transform as a solution to coarse scale template matching, where alignment concerns between decimation of a target and decimation of a larger search image can be mitigated, and computational efficiency can be maintained. Furthermore, template matching with ILP coefficients can provide several intuitive "near-matches" that may be of interest in image retrieval applications.
The statistics of natural scenes in the wavelet domain are accurately characterized by the Gaussian scale mixture (GSM) model. The model lends itself easily to analysis and many applications that use this model are em...
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The statistics of natural scenes in the wavelet domain are accurately characterized by the Gaussian scale mixture (GSM) model. The model lends itself easily to analysis and many applications that use this model are emerging (e.g., denoising, watermark detection). We present an error-resilient image communications application that uses the GSM model and multiple description coding (MDC) to provide error-resilience. We derive a rate-distortion bound for GSM random variables, derive the redundancy rate-distortion function, and finally implement an MD image communication system.
In wavelets based coding applications, resolution scalability is achieved by retaining the low pass signal subband corresponds to the required resolution and discarding other high pass wavelet subbands. Aliasing is a ...
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In wavelets based coding applications, resolution scalability is achieved by retaining the low pass signal subband corresponds to the required resolution and discarding other high pass wavelet subbands. Aliasing is a common problem present in such downsampling. In this paper a novel technique for improving the low pass filter for improved downsampling is presented. This method uses an extra update step followed by P+U lifting scheme. The preprocessing update step is chosen as the dual update step associated with the wavelet. The spatially adaptive low pass (SALP) filtering concept is used for the second update step, leading to an overall low pass filter whose size adapts to the underlying signal content. The filter choices for the second update step is recovered at the decoder without any bookkeeping. Results using the 2D 5/3 wavelet with the extra pre-processing update step show improvements over conventional wavelets.
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