Browsing by Author "Lang, Markus"

Now showing 1 - 19 of 19
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    Allpass Filter Design and Applications
    (1995-01-15) Lang, Markus; Digital Signal Processing (http://dsp.rice.edu/)
    The Problem of allpass filter design for phase approximation and equalization in the Chebyshev sense is solved by using a generalized Remez algorithm. Convergence to the unique optimum is guaranteed and is achieved rapidly in the actual implementation. The well-known numerical problems for higher degree filters are analyzed and solved by a simple approach. Possible applications are: design of filters with a desired phase response (e.g., a delay element), the design of phase equalizers, or the design of recursive filters with magnitude prescriptions using parallel allpass filters. For the latter the algorithm can be modified to allow arbitrary tolerance schemes for the magnitude response.
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    Constrained Least Square Design of FIR Filters Without Specified Transition Bands
    (1996-01-15) Selesnick, Ivan W.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    We consider the design of digital filters and discuss the inclusion of explicitly specified transition bands in the frequency domain design of FIR filters. We put forth the notion that explicitly specified transition bands have been introduced in the filter design literature as an indirect and sometimes inadequate approach for dealing with discontinuities in the desired frequency response. We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR filters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR filters and gives the best L2 filter and a continuum of Chebyshev filters as special cases.
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    Constrained Least Square Design of FIR Filters Without Specified Transition Bands
    (1995-01-15) Selesnick, Ivan W.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    We consider the design of digital filters and discuss the inclusion of explicitly specified transition bands in the frequency domain design of FIR filters. We put forth the notion that explicitly specified transition bands have been introduced in the filter design literature as an indirect and sometimes inadequate approach for dealing with discontinuities in the desired frequency response. We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR filters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR filters and gives the best L2 filter and a continuum of Chebyshev filters as special cases.
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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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    Magnitude Squared Design of Recursive Filters with the Chebyshev Norm Using a Constrained Rational Remez Algorithm
    (1994-10-01) Selesnick, Ivan W.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    We describe a Remez type exchange algorithm for the design of stable recursive filters for which the Chebyschev norm of H(w) - F(w) is minimized, where H(w) and F(w) are the realized and desired magnitude squared frequency responses. The number of poles and zeros can be chosen arbitrarily and the zeros do not have to lie on the unit circle. The algorithm allows us to design filters with non-conventional frequency responses with arbitrary weighting functions. It also gives optimal minimum phase FIR filters and Elliptic recursive filters as special cases. We discuss three main difficulties in the use of the Remez algorithm for recursive filter design and give ways to overcome them.
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    Magnitude Squared Design of Recursive Filters with the Chebyshev Norm Using a Constrained Rational Remez Algorithm
    (1994-05-01) Selesnick, Ivan W.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    We describe a Remez type exchange algorithm for the design of stable recursive filters for which the Chebyschev norm of H(w) - F(w) is minimized, where H(w) and F(w) are the realized and desired magnitude squared frequency responses. The number of poles and zeros can be chosen arbitrarily and the zeros do not have to lie on the unit circle. The algorithm allows us to design filters with non-conventional frequency responses with arbitrary weighting functions. It also gives optimal minimum phase FIR filters and Elliptic recursive filters as special cases. We discuss three main difficulties in the use of the Remez algorithm for recursive filter design and give ways to overcome them.
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    A New and Efficient Program for Finding All Polynomial Roots
    (1993-01-15) Lang, Markus; Frenzel, Bernhard-Christian; Digital Signal Processing (http://dsp.rice.edu/)
    Finding polynomial roots rapidly and accurately is an important problem in many areas of signal processing. We present a new program which is a combination of Muller's and Newton's method. We use the former for computing a root of the deflated polynomial which is a good estimate for the root of the original polynomial. This estimate is improved by applying Newton's method to the original polynomial. Test polynomials up to the degree 10000 show the superiority of our program over the best methods to our knowledge regarding speed and accuracy, i.e., Jenkins/Traub program and the eigenvalue method. Furthermore we give a simple approach to improve the accuracy for spectral factorization in the case there are double roots on the unit circle. Finally we briefly consider the inverse problem of root finding, i.e., computing the polynomial coefficients from the roots which may lead to surprisingly large numerical errors.
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    Noise Reduction Using an Undecimated Discrete Wavelet Transform
    (1995-01-15) Lang, Markus; Guo, Haitao; Odegard, Jan E.; Burrus, C. Sidney; Wells, R.O.; Digital Signal Processing (http://dsp.rice.edu/)
    A new nonlinear noise reduction method is presented that uses the discrete wavelet transform. Similar to Donoho and Johnstone, we employ thresholding in the wavelet transform domain but, following a suggestion by Coifman, we use an undecimated, shift-invariant, nonorthogonal wavelet transform instead of the usual orthogonal one. This new approach can be interpreted as a repeated application of the original Donoho and Johnstone method for different shifts. The main feature of the new algorithm is a significantly improved noise reduction compared to the original wavelet based approach, both the l2 error and visually, for a large class of signals. This is shown both theoretically as well as by experimental results.
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    Nonlinear phase FIR filter design with minimum LS error and additional constraints
    (1994-07-01) Lang, Markus; Bamberger, Joachim; Digital Signal Processing (http://dsp.rice.edu/)
    We examine the problem of approximating a complex frequency response by a real-valued FIR filter according to the L2 norm subject to additional inequality constraints for the complex error function. Starting with the Kuhn-Tucker optimality conditions which specialize to a system of nonlinear equations we deduce an iterative algorithm. These equations are solved by Newton's method in every iteration step. The algorithm allows arbitrary tradeoffs between an L2 and an Loo design. The L2 and the Loo solution result as special cases.
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    Nonlinear Processing of a Shift Invariant DWT for Noise Reduction
    (1995-04-20) Lang, Markus; Guo, Haitao; Odegard, Jan E.; Burrus, C. Sidney; Wells, R.O.; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelet transform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach, both in terms of the l2 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.
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    Nonlinear Processing of a Shift Invariant DWT for Noise Reduction
    (1995-03-20) Lang, Markus; Guo, Haitao; Odegard, Jan E.; Burrus, C. Sidney; Wells, R.O.; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelet transform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach, both in terms of the l2 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) 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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    Polynomial Root Finding
    (1994-10-01) Lang, Markus; Frenzel, Bernhard-Christian; Digital Signal Processing (http://dsp.rice.edu/)
    Finding polynomial roots rapidly and accurately is an important problem in many areas of signal processing. We present a program which is superior in speed and accuracy to the best methods to our knowledge, i.e., Jenkins/Traub program and the eigenvalue method. Based on this we give a simple approach to improve the accuracy for spectral factorization in the case there are double roots on the unit circle.
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    Simultaneous Speckle Reduction and Data Compression using Best Wavelet Packet Bases with Applications to SAR based ATD/R
    (1995-04-20) Wei, Dong; Guo, Haitao; Odegard, Jan E.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    We propose a novel method for simultaneous speckle reduction and data compression based on shrinking, quantizing and coding the wavelet packet coefficients of the logarithmically transformed image. A fast algorithm is used to find the best wavelet packet basis in the rate-distortion sense from the entire library of admissible wavelet packet bases. Soft-thresholding in wavelet domain can significantly suppress the speckles of the synthetic aperture radar (SAR) images while maintaining bright reflections for subsequent detection and recognition. Optimal bit allocation, quantization and entropy coding achieve the goal of compression while maintaining the fidelity of the SAR image.
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    Wavelet Based SAR Speckle Reduction and Image Compression
    (1995-01-15) Odegard, Jan E.; Guo, Haitao; Lang, Markus; Burrus, C. Sidney; Wells, R.O.; Novak, L.M.; Hiett, M.; Digital Signal Processing (http://dsp.rice.edu/)
    This paper evaluates the performance of the recently published wavelet based algorithm for speckle reduction of SAR images. The original algorithm, based on the theory of wavelet thresholding due to Donoho and Johnstone, has been shown to improve speckle statistics. In this paper we give more extensive results based on tests performed at Lincoln Laboratory (LL). The LL benchmarks show that the SAR imagery is significantly enhanced perceptually. Although the wavelet processed data results in an increase in the number of natural clutter false alarms (from trees etc.) an appropriately modified CFAR detector (i.e., by clamping the estimated clutter standard deviation) eliminates the extra false alarms. The paper also gives preliminary results on the performance of the new and improved wavelet denoising algorithm based on the shift invariant wavelet transform. By thresholding the shift invariant discrete wavelet transform we can further reduce speckle to achieve a perceptually superior SAR image with ground truth information significantly enhanced. Preliminary results on the speckle statistics of this new algorithm is improved over the classical wavelet denoising algorithm. Finally, we show that the classical denoising algorithm as proposed by Donoho and Johnstone and applied to SAR has the added benefit of achieving about 3:1 compression with essentially no loss in image fidelity.
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    Wavelet Based SAR Speckle Reduction and Image Compression
    (1995-04-01) Odegard, Jan E.; Guo, Haitao; Lang, Markus; Burrus, C. Sidney; Wells, R.O.; Novak, L.M.; Hiett, M.; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)
    This paper evaluates the performance of the recently published wavelet based algorithm for speckle reduction of SAR images. The original algorithm, based on the theory of wavelet thresholding due to Donoho and Johnstone, has been shown to improve speckle statistics. In this paper we give more extensive results based on tests performed at Lincoln Laboratory (LL). The LL benchmarks show that the SAR imagery is significantly enhanced perceptually. Although the wavelet processed data results in an increase in the number of natural clutter false alarms (from trees etc.) an appropriately modified CFAR detector (i.e., by clamping the estimated clutter standard deviation) eliminates the extra false alarms. The paper also gives preliminary results on the performance of the new and improved wavelet denoising algorithm based on the shift invariant wavelet transform. By thresholding the shift invariant discrete wavelet transform we can further reduce speckle to achieve a perceptually superior SAR image with ground truth information significantly enhanced. Preliminary results on the speckle statistics of this new algorithm is improved over the classical wavelet denoising algorithm. Finally, we show that the classical denoising algorithm as proposed by Donoho and Johnstone and applied to SAR has the added benefit of achieving about 3:1 compression with essentially no loss in image fidelity.
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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.