Browsing by Author "Gopinath, Ramesh A."

Now showing 1 - 13 of 13
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    Design of Linear Phase Cosine Modulated Filter Banks for Subband Image Compression
    (1994-01-15) Odegard, Jan E.; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    Wavelet methods give a flexible alternative to Fourier methods in non-stationary signal analysis. The concept of band-limitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scale-limitedness. Obvious definitions of scale-limitedness are too restrictive, in that there would be few or no useful scale-limited signals. This paper introduces a viable definition for scale-limited signals, and shows that the class is rich enough to include bandlimited signals, and impulse trains, among others. Moreover, for a wide choice of criteria, we show how to design the optimal wavelet for representing a given signal, and how to design robust wavelets that optimally represent certain classes of signals.
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    Enhancement of Decompressed Images at Low Bit Rates
    (1994-07-20) Gopinath, Ramesh A.; Lang, Markus; Guo, Haitao; Odegard, Jan E.; Digital Signal Processing (http://dsp.rice.edu/)
    Transform coding at low bit rates introduces artifacts associated with the basis functions of the transform. For example, decompressed images based on the DCT (discrete cosine transform)- like JPEG16 - exhibit blocking artifacts at low bit rates. This paper proposes a post-processing scheme to enhance decompressed images that is potentially applicable in several situations. In particular, the method works remarkable well in "deblocking" of DCT compressed images. The method is non-linear, computationally efficient, and spatially adaptive - and has the distint feature that it removes artifacts while yet retaining sharp features in the images. An important implication of this result is that images coded using the JPEG standard can be efficiently post-processed to give significantly improved visual quality in the images.
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    Nonlinear Wavelet Processing for Enhancement of Images
    (1994-05-20) Odegard, Jan E.; Lang, Markus; Guo, Haitao; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    In this note we apply some recent results on nonlinear wavelet analysis to image processing. In particular we illustrate how the (soft) thresholding algorithm due to Donoho and Johnstone can successfully be used to remove speckle in SAR imagery. Furthermore, we also show that transform coding artifacts, such as blocking in the JPEG algorithm, can be removed to achieve a perceptually improved image by post-processing the decompressed image.
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    On the Correlation Structure of Multiplicity M Scaling Functions and Wavelets
    (1992-05-20) Gopinath, Ramesh A.; Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    None
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    On the Correlation Structure of Multiplicity M Scaling Functions and Wavelets
    (1992-01-15) Gopinath, Ramesh A.; Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    In this paper we study the auto-correlation and cross-correlation structure of the scaling and wavelet functions associated with compactly supported orthonormal wavelet basis. These correlation structures play an important role in both wavelet-based interpolation and in answering the question of existence of scale-limited signals. Our investigations into their nature, gives us a fairly complete account of all the zeros of the correlation functions and also give efficient algorithms for their computation. An interesting fact that arises from the analysis is that all the correlations possible have infinitely many zeros in their support.
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    On the Moments of the Scaling Function psi_0
    (1992-05-20) Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    This paper derives relationships between the moments of the scaling function psi0(t) associated with multiplicity M, K-regular, compactly supported, orthonormal wavelet bases [6, 5] that are extensions of the multiplicity 2, K-regular orthonormal wavelet bases constructed by Daubechies. One such relationship is that the square of the first moment of the scaling function (psi0(t)) is equal to its second moment. This relationship is used to show that uniform sample values of a function provides a third order approximation of its scaling function expansion coefficients. For the special case of M=2, the results in this paper have been reported earlier.
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    On the Moments of the Scaling Function psi_0
    (1992-01-15) Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    This paper derives relationships between the moments of the scaling function psi_0(t) associated with multiplicity M, K-regular, compactly supported, orthonormal wavelet bases [6, 5] that are extensions of the multiplicity 2, K-regular orthonormal wavelet bases constructed by Daubechies. One such relationship is that the square of the first moment of the scaling function (psi_0(t)) is equal to its second moment. This relationship is used to show that uniform sample values of a function provides a third order approximation of its scaling function expansion coefficients. For the special case of M=2, the results in this paper have been reported earlier.
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    Optimal wavelets for signal decomposition and the existence of scale limited signals
    (1992-05-20) Odegard, Jan E.; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    Wavelet methods give a flexible alternative to Fourier methods in non-stationary signal analysis. The concept of band-limitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scale-limitedness. Obvious definitions of scale-limitedness are too restrictive, in that there would be few or no useful scale-limited signals. This paper introduces a viable definition for scale-limited signals, and shows that the class is rich enough to include bandlimited signals, and impulse trains, among others. Moreover, for a wide choice of criteria, we show how to design the optimal wavelet for representing a given signal, and how to design robust wavelets that optimally represent certain classes of signals.
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    Optimal wavelets for signal decomposition and the existence of scale limited signals
    (1992-01-15) Odegard, Jan E.; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    Wavelet methods give a flexible alternative to Fourier methods in non-stationary signal analysis. The concept of band-limitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scale-limitedness. Obvious definitions of scale-limitedness are too restrictive, in that there would be few or no useful scale-limited signals. This paper introduces a viable definition for scale-limited signals, and shows that the class is rich enough to include bandlimited signals, and impulse trains, among others. Moreover, for a wide choice of criteria, we show how to design the optimal wavelet for representing a given signal, and how to design robust wavelets that optimally represent certain classes of signals.
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    Theory of Regular M-band Wavelet Bases
    (1993-12-20) Steffen, P.; Heller, Peter Niels; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    This paper constructs K-regular M-band orthonormal wavelet bases. K-regularity of the wavelet basis is known to be useful in numerical analysis applications and in image coding using wavelet techniques. Several characterizations of K-regularity and their importance are described. An explicit formula is obtained for all minimal length M-band scaling filters. A new state-space approach to constructing the wavelet filters from the scaling filters is also described. When M-band wavelets are constructed from unitary filter banks they give rise to wavelet tight frames in general (not orthonormal bases). Conditions on the scaling filter so that the wavelet bases obtained from it is orthonormal is also described.
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    Wavelet Based Speckle Reduction with Applications to SAR based ATD/R
    (1994-11-20) Guo, Haitao; Odegard, Jan E.; Lang, Markus; Gopinath, Ramesh A.; Selesnick, Ivan W.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    This paper introduces a novel speckle reduction method based on thresholding the wavelet coefficients of the logarithmically transformed image. The method is computational efficient and can sinificantly reduce the speckle while preserving the resolution of the original image. Both soft and hard thresholding schemes are studied and the results are compared. When fully polarimetric SAR images are available, we proposed several approaches to combine the data from different polorizations to achieve even better performance. Wavelet processed imagery is shown to provide better detection performance for synthetic-aperture radar (SAR) based automatic target detection/recognition (ATD/R)problem.
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    Wavelet-Based Post-Processing of Low Bit Rate Transform Coded Images
    (1994-01-15) Gopinath, Ramesh A.; Lang, Markus; Guo, Haitao; Odegard, Jan E.; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    In this paper we propose a novel method based on wavelet thresholding for enhancement of decompressed transform coded images. Transform coding at low bit rates typically introduces artifacts associated witht he basis functions of the transform. In particular, the method works remarkably well in "deblocking" of DCT compressed images. The method is nonlinear, computationally efficient, and spatially adaptive and has the distinct feature that it removes artifacts yet retain sharp features in the images. An important implication of this result is that iamges coded using the JPEG standard can efficiently be postprocessed to give significantly improved visual quality in the images. The algorithm can use a conventional JPEG encoder and decoder for which VLSI chips are available.
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    Wavelet-Based Post-Processing of Low Bit Rate Transform Coded Images
    (1994-11-01) Gopinath, Ramesh A.; Lang, Markus; Guo, Haitao; Odegard, Jan E.; Digital Signal Processing (http://dsp.rice.edu/)
    In this paper we propose a novel method based on wavelet thresholding for enhancement of decompressed transform coded images. Transform coding at low bit rates typically introduces artifacts associated witht he basis functions of the transform. In particular, the method works remarkably well in "deblocking" of DCT compressed images. The method is nonlinear, computationally efficient, and spatially adaptive and has the distinct feature that it removes artifacts yet retain sharp features in the images. An important implication of this result is that iamges coded using the JPEG standard can efficiently be postprocessed to give significantly improved visual quality in the images. The algorithm can use a conventional JPEG encoder and decoder for which VLSI chips are available.