EECS 556 W05 Lecture Topics - Jeff Fessler This list will be updated regularly (online) over the course of the semester. Lecture# topic (x.x.x indicate sections from text by Lim) 1 course policies *** 2D CONTINUOUS-SPACE SIGNALS/SYSTEMS signal transformations signal classes (symmetry, periodic) 2D impulse function / properties 2D systems, input-output relationship system classifications A-2 stability A-3 invertibility S-1 causality S-1' separability S-2 memory 2 S-3 shift-invariance S-4 rotation-invariance A-1 linearity point spread function (PSF)/ impulse response impulse representation superposition property convolution convolution properties system properties in terms of PSF: causality, memory, stability, invertibility, rotation invariance 3 orthogonal representation of signals generalized Fourier series ideas behind Fourier coefficient formula Parseval's theorem separable bases 1D FS example (Harr) 2D Fourier series eigenfunctions FS convergence (skip) Gibbs phenomenon (skip) completeness properties of FS (skip) FS time transformation differentiation property modulation property linearity filtering Fourier series through LSI FS of impulse train (comb) and "bed of nails" 2D FS example 2D Fourier transform existence of FT (skip) FT examples (skip) Properties of 2D FT linearity convolution correlation shift magnification (scaling) duality differentiation parseval's theorem symmetry properties (even, real) 2D-FT of periodic functions New properties rotation rotational symmetry separability circular symmetry 4 Hankel transform OTF/MTF 2D-FT Examples rms bandwidth, rms time duration time-bandwidth product, gaussian example Sampling rectilinear sampling nyquist sampling rate / sampling theorem aliasing sinc interpolation 5 video interpolation 2D-DSFT / 2D-FT relationship 2D DFT/FFT, relationships to 2D-FT fftshift 6 *** Optical imaging basics Fourier transforming property of lenses Imaging property of lenses (PSF, frequency response) *** C1. 2D discrete-space signals/systems 2D Kronecker impulse function / properties notation, coordinate systems signal classes (symmetry, periodic, separable) circular symmetry 7 2D systems, input-output relationship system classifications A-2 stability A-3 invertibility S-1 causality S-1' separability S-2 memory S-3 shift-invariance S-4 rotation-invariance A-1 linearity impulse response convolution sum graphical convolution separable convolution edge effects convolution properties correlation system properties in terms of PSF: causality, memory, stability, invertibility, rotation invariance 8 eigenfunctions 2D discrete-space Fourier transform existence/convergence of FT periodic signals properties LSI systems in frequency domain magnitude vs phase phase-only reconstruction / magnitude retrieval sampling revisited filters introduction to filter design separability vs rotation invariance 9 *** C4 FIR filters 4.1 zero phase symmetries computation 4.2 filter specs ideal filter impulse response filtering using FFT Discrete Fourier series discrete-space orthogonal representation properties 10 circular convolution circular convolution example DFT 3 imperfect perspectives: orthonormal basis, periodization, sampling DSFT derivation properties 11 circular convolution relationship to DSFT zero padding overlap-add method sampling dsft 12 sampling H(omega) example matrix representation of DFT DCT motivation 13 derivation properties FFT row column decomposition *** C8 Image enhancement Contrast adjustment piecewise linear contrast adjustment 14 histograms histogram transformation Noise smoothing linear vs median filters 15 median statistics Image interpolation nearest, sinc, bilinear 16 interpolator properties b-splines (exam 1) 17 (yendiki) Edge detection gradient-based methods derivatives from discrete images laplacian-based methods marr and hildreth methods parametric edge-detection methods canny's method 18 B-spline interpolation 19 cardinal B-splines Motion estimation Motion-compensated interpolation region matching methods 20 space-time constraint equation temporal interpolation Pseudo-color / false color (skip) *** C6 Spectral estimation (random field image models) random vectors (winter break) 21 random processes, WSS autocorrelation, cross-correlation power spectral density RP's through LSI systems Noncausal Wiener filter 22 Spectral estimation periodogram cross-correlation and windowing nonnegativity of power spectra 23 autocorrelation functions for filtered point process *** C9 Image restoration overview degradation estimation motion blur 24 noise removal Wiener filter and variations Review of periodogram and spectral estimation adaptive image processing adaptive Wiener filter noise visibility (skim) short-space spectral subtraction (skim) edge-sensitive adaptation (skim) blur removal (skim) Wiener filter form (hw) reduction of signal-dependent noise (skim) temporal filtering (skim) 25 *** CR Statistical methods for image restoration (not in text!) matrix-vector representations of convolution diagonalization of circulant matrices vs DFT inverse filter / deconvolution (in both SP and matrix forms) 26 statistical formulations: MMSE, MAP, maximum likelihood gaussian MAP restoration 27 circulant analysis penalized least squares roughness penalties differencing matrix C 28 circulant analysis mean and variance analysis PLS case, general linear case circulant analysis resolution-noise tradeoff nonquadratic PLS edge-preserving penalty functions nonlinear estimation as adaptive penalty weighting 29 algorithms for NPLS optimization transfer, surrogate functions paraboloidal surrogate algorithm DePierro's trick for separating (skipped) 30 separable paraboloidal surrogate (SPS) algorithm npls_sps.m explanation sparse matrix representation (skipped) skipped: phase-retrieval (Gerchberg-Saxton) super-resolution (Gerchberg-Papoulis) 31 *** C10: Image coding quantization scalar quantization (uniform) quantizer design (nonuniform) companding 32 vector quantization codebook design 33 codeword assignment bit allocation uniform length variable length Huffman, entropy waveform coding PCM Robert's pseudonoise skim: delta mod., diff PCM, two-channel k-means (LBG) algorithm ------- we covered at least up to here, below from W01 in T/Th format ------ (exam 2) 34 pyramid coding 25 skim: adaptive coding analysis of Laplacian pyramid transform coding KL transform KL derivation (brief) 26 JPEG standard, which addresses: other transforms practical issues subimages zones / bit allocation artifacts hybrid transform coding adaptive coding model coding (skip) interframe coding (skip) (course evaluations) 27 introduction to shape statistics (+ Mardia lecture) 28 binary morphology Dec. 1999 T-IP issue ---------------- other topics we could cover if there is time... image segmentation wavelet coefficient thresholding wavelet image coding image analysis deformable templates object recognition