| Name of the article | Name of the plan | Short description |
| Fourier transform 2D | Properties | Those are presented: linearity, separability, translation, substitution, rotation, differentiation, scaling... |
| Why wavelets? | Introduction | The challenge: how to localize given signal both in time and frequency? |
| Fourier transform | Maybe we use Fourier transform...? | |
| Windowed Furier transform | Or windowed Fourier transform? | |
| Gabor transform | Or gabor transform... | |
| Relative frequency analysis | Lets change the width of the window according to the changes in the signal... | |
| Wavelet transform | Here you will see that wavelet transform the best can localize our signal in time and frequency. | |
| Mathematical basics | Basis functions | What are basis functions? How do they look like? How do wavelets look like? What is scaling function and mother wavelet? |
| Dilation equation | The heart of wavelet method - the basic formula. | |
| Definitions | A couple of definitions for mother wavelet and scaling function. What is normality, orthogonality, orthonormality? What are vanishing moments of the wavelet? Conditions that wavelets must fulfil. | |
| How to make a wavelet | A simple simulation: shows how wavelet is created from shifted, scaled and translated versions of scaling function. On examples of Haar, Daubechies and Coifflet wavelets. | |
| Wavelet transform | What is wavelet transform and inverse wavelet transform? Formulas, definitions. The notion of decomposition, coefficients, high-pass and low-pass filters. Filter conditions, quadrature mirror filters. | |
| Fast wavelet transform | Fast wavelet transform (FWT) - tree algorithm. Comparison of computational complexity of discrete fourier transform (DFT), fast Fourier transform (FFT) and fast wavelet transform. | |
| Decomposition | Decomposition | What is a decomposition? Decomposition of two dimensional image and a vector using a low-pass and high-pass filters. |
| Low pass filter | How works low-pass filtering? On example of Haar wavelets. | |
| High pass filter | How works high-pass filtering? On example of Haar wavelets. | |
| How to do the decomposition | How to do the decomposition of two dimensional image? Successive using of H and L filters for proper parts of image. | |
| Reconstruction | The inverse process to decomposition. Reconstruction of one dimensional vector and image. Filters L* and H* of the inverse transform. | |
| Multiresolution analysis MRA | Progressive transmission | The application of multiresolution analysis - how effectively send images from the database to the remote computer? |
| MRA definitions | Definitions of spaces V and W: upward completeness, downward completeness, scale invariance, shift invariance, existence of a basis . | |
| Multiresolution analysis | Interactive simulation. User can choose between one dimensional (line from an image) and two dimensional (image) signal , the type of wavelets and choose if space is spanned by scaling functions or wavelets. At the same time one can see changing spaces (subspaces). Progressive transmission. | |
| Wavelet compression | Why compression? | What is compression? Why do we need it? Examples. Lossless and lossy compression. |
| Before and after compression... | Run Length Encoding (RLE) method, histograms of signal before and after wavelet transform. | |
| Compression schema |
Algorithm of compression: decomposition (conditions, examples of wavelets used in compression), quantization (what it is, the idea of scalar and vector quantization, codebook) and encoding (the idea of encoding, Huffman coding). Image before and after process of lossy compression. |
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| Comparison | Definitions of compression ratio, Root Mean Square Error, Peak signal-To-Noise Ratio. Comparison of images compressed with wavelets and JPEG. |