Comments on "phase-shifting for nonseparable 2-D haar wavelets"

In their recent paper, Alnasser and Foroosh derive a wavelet-domain (in-band) method for phase-shifting of 2-D "nonseparable" Haar transform coefficients. Their approach is parametrical to the (a priori known) image translation. In this correspondence, we show that the utilized transform is in fact the separable Haar discrete wavelet transform (DWT). As such, wavelet-domain phase shifting can be performed using previously-proposed phase-shifting approaches that utilize the overcomplete DWT (ODWT), if the given image translation is mapped to the phase component and in-band position within the ODWT

Segmentwise Discrete Wavelet Transform

Dizertační práce se zabývá algoritmy SegDWT pro segmentový výpočet Diskrétní Waveletové Transformace – DWT jedno i vícedimenzionálních dat. Segmentovým výpočtem se rozumí způsob výpočtu waveletové analýzy a syntézy po nezávislých segmentech (blocích) s určitým překryvem tak, že nevznikají blokové artefakty. Analyzující část algoritmu pracuje na principu odstranění přesahu a produkuje vždy část waveletových koeficientů z waveletové transformace celého signálu, které mohou být následně libovolně zpracovány a podrobeny zpětné transformaci. Rekonstruované segmenty jsou pak skládány podle principu přičtení přesahu. Algoritmus SegDWT, ze kterého tato práce vychází, není v současné podobně přímo použitelný pro vícerozměrné signály. Tato práce obsahuje několik jeho modifikací a následné zobecnění pro vícerozměrné signály pomocí principu separability. Kromě toho je v práci představen algoritmus SegLWT, který myšlenku SegDWT přenáší na výpočet waveletové transformace pomocí nekauzálních struktur filtrů typu lifting.The dissertation deals with SegDWT algorithms performing a segmented (segmentwise) computation of one- and multi-dimensional Discrete Wavelet Transform – DWT. The segmented approach allows one to perform the segment (block) wavelet analysis and synthesis using segment overlaps while preventing blocking artifacts. The parts of the wavelet coefficients of the whole signal wavelet transform corresponding to the actual segment are produced by the analysis part of the algorithm exploiting overlap-save principle. The resulting coefficients belonging to the segment can be processed arbitrarily and than they can transformed back to the original domain. The reconstructed segments are than put together using overlap add principle. The already known SegDWT algorithm can not be effectively used on multidimensional signals. Several modifications of the algorithm are proposed which makes it possible to generalize it to multidimensional cases using separability property. In addition, the thesis presents SegLWT algorithm adopting ideas of the SegDWT and transferring it to the non-causal lifting filter bank structures.

Integrasi Discrete Wavelet Transform dan Singular Value Decomposition pada Watermarking Citra untuk Perlindungan Hak Cipta

Tren masalah watermarking pada sekarang ini adalah bagaimana mengoptimalkan trade-off antara imperceptibility (visibilitas) citra ter-watermark terhadap pengaruh distorsi dan robustness terhadap penyisipan watermark. Masalah menggunakan kekuatan penyisipan berdasarkan Single Scaling Factor (SSF) atau Multiple Scaling Factor (MSF) juga ditemukan. Penelitian ini mengusulkan metode penyisipan watermark untuk perlindungan hak cipta pada citra dan algoritma ekstraksi citra ter-watermark yang dioptimalkan dengan penggabungan Discrete Wavelet Transform (DWT) dan Singular Value Decomposition (SVD). Nilai-nilai singular dari LL3 koefisien sub-band dari citra host dimodifikasi menggunakan nilai tunggal citra watermark biner menggunakan MSFs. Kontribusi utama dari skema yang diusulkan adalah aplikasi DWT-SVD untuk mengidentifikasi beberapa faktor skala yang optimal. Hasil penelitian menunjukkan bahwa skema yang diusulkan menghasilkan nilai Peak Signal to Noise Ratio (PSNR) yang tinggi, yang menunjukkan bahwa kualitas visual gambar yang baik pada masalah citra watermarking telah mengoptimalkan trade-off. Trade-off antara imperceptibility (visibilitas) citra ter-watermark terhadap pengaruh distorsi dan robustness citra ter-watermark terhadap operasi pengolahan citra. Nilai PSNR yang didapat pada citra yang diujikan: baboon=53,184; boat=53,328; cameraman=53,700; lena=53,668; man=53,328; dan pepper sebesar 52,662. Delapan perlakuan khusus pada hasil citra ter-watermark diujikan dan diekstraksi kembali yaitu JPEG 5%, Noise 5%, Gaussian filter 3x3, Sharpening, Histogram Equalization, Scaling 512-256, Gray Quantitation 1bit, dan Cropping 1/8. Hasil dari perlakuan khusus kemudian diukur nilai Normalized Cross-Correlation (NC) yang menghasilkan rata-rata semua citra diperoleh sebesar 0,999 dari satu. Hasil penelitian dari metode yang diusulkan lebih unggul nilai PSNR dan NC dari penelitian sebelumnya. Jadi dapat disimpulkan bahwa penerapan dengan metode DWT-SVD ini mampu menghasilkan citra yang robust namun memiliki tingkat imperceptibility yang cukup tinggi

Wavelets and their use

This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to corresponding literature. The multiresolution analysis and fast wavelet transform became a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for achievement of a goal. Analysis of various functions with the help of wavelets allows to reveal fractal structures, singularities etc. Wavelet transform of operator expressions helps solve some equations. In practical applications one deals often with the discretized functions, and the problem of stability of wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves by some examples only. The authors would be grateful for any comments which improve this review paper and move us closer to the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh