Author
Guanqun Chen
Bio: Guanqun Chen is an academic researcher. The author has contributed to research in topics: Semidefinite programming & Filter (signal processing). The author has an hindex of 1, co-authored 1 publications receiving 1 citations.
Papers
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01 Jan 2010
TL;DR: In this paper, a second-order cone programming (SOCP) optimization approach is proposed for the design of M th-band filters, which is more appropriate for the 2-D M thband filter design than the SOCP approach because of its efficient and simple optimization structure.
Abstract: Cone programming (CP) is a class of convex optimization technique, in which a linear objective function is minimized over the intersection of a set of affine constraints. Such constraints could be linear or convex, equalities or inequalities. Owing to its powerful optimization capability as well as flexibility in accommodating various constraints, the cone programming finds wide applications in digital filter design. In this thesis, fundamentals of linear-phase M th-band FIR filters are first introduced, which include the time-domain interpolation condition and the desired frequency specifications. The restriction of the interpolation matrix M for linear-phase two-dimensional (2-D) M th-band filters is also discussed by considering both the interpolation condition and the symmetry of the impulse response of the 2-D filter. Based on the analysis of the M th-band properties, a semidefinite programming (SOP) optimization approach is developed to design linear-phase 1-0 and 2-D M th-band filters. The 2-D SOP optimization design problem is modeled based on both the mini-max and the least-square error criteria. In contrast to the 1-D based design, the 2-D direct SDP design can offer an optimal equiripple result. A second-order cone programming (SOCP) optimization approach is then presented as an alternative for the design of M th-band filters. The performances as well as the design complexity of these two design approaches are justified through numerical design examples. Simulation results show that the performance of the SOCP approach is better than that of the SDP approach for 1-D M th-band filter design due to its reduced computational complexity for the worst-case, whereas the SDP approach is more appropriate for the 2-D M th-band filter design than the SOCP approach because of its efficient and simple optimization structure. Moreover, the designed M th-band filters are proved useful in image interpolation according to both the visual quality and the peak signal-to-noise ratio (PSNR) for the images with different levels of details.
1 citations
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01 Nov 1985TL;DR: You must turn in your code as well as output files to generate a report that contains the code and ouput in a single readable format.
Abstract: You must turn in your code as well as output files. Please generate a report that contains the code and ouput in a single readable format. Getting Started You may want to download Irfanview image viewing software. It handles pretty much any image type, lets you convert, and provides batch processing. Download the sample images from the class website. The following question operates on the city.jpg image. (a) Perform image smoothing using a 7×7 averaging filter and a Gaussian filter with σ = 0.5 and 3. Compare the outputs. (b) Perform edge enhancement using the Sobel operator (Matlab's default parameters). Repeat using the Laplacian and Laplacian of Guassian operators. Compare the outputs 2. Frequency Domain Filtering The following question operates on the city.jpg image. (a) Find the Fourier transform of the image. Be sure to center the frequencies. (b) Perform image smoothing in the frequency domain using the filters defined in the previous problem. Compare the output images from the two methods (spatial and frequency) and the time for operation. (c) Perform edge enhancement using the filters defined in the previous problem. (d) Define a lowpass filter in the frequency domain with radius of 1/4 the height. Show the result. Repeat with a similar sized Guassian and compare the results. Give the σ parameter you used and show the output transform image. (e) Repeat with a rectangular filter with the same dimension as the ideal lowpass. Compare the results between the ideal filter and the rectangular approximation. 3. Canny Edge Detection (a) Give the convolution kernels for determining the gradient. You may examine the function gradient.m to help with the explanation. (It may be easiest to apply the gradient to an impulse and inspect the results. (b) Implement the simplified version of the Canny edge detector (single scale). The syntax of the function should be where E contains the detected edges, M the smoothed gradient magnitude, A contains the gradient angle, I is the input image, sig is the σ parameter for the smoothing filter, and tau= [τ h , τ l ] is the two element vector containing the hysteresis thresholds. See Algorithm 6.4 for non-maximal suppression and Algorithm 6.5 for hysteresis thresh-olding. (It may be more efficient to implement the hysteresis as edge tracking)
285 citations