Wavelets and science

Wavelet is a novel scientific idea and method that has been rapidly developed and increasingly perfected since its emergence in the 1980s. It is the selfless contribution of many scientists and engineers in the contemporary mainstream scientific research field to exhaust their outstanding wisdom and contribute to the treasure house of human thoughts and cognitive methods. A majestic scientific symphony chapter. The wavelet method has localization capabilities in both the observation domain and the transformation domain. Its wide application has promoted mathematics, physics, computer science, optics, acoustics, biology and medicine, information science, control science, visual science, quantum theory, Scientific concepts and ideas, epistemology and calculation methods in the main frontier fields of contemporary science and technology, including astrophysics, management, precision mechanics and aerospace science, have entered a new era, with fruitful results and large-scale innovations achieved. Wavelet theory also enjoys the reputation of "mathematical microscope".
The course "Wavelets and Science" is aimed at college students, graduate students and scientific researchers who are in their second year of study in science, engineering, management, medicine and other disciplines and have experience in learning linear algebra and calculus. It plans to introduce the wavelet method to solve contemporary problems through 24 hours of study. Typical successful cases of research issues in mainstream frontier fields of science and technology, helping learners understand and master the scientific ideas and research methods of the core wavelet theory, such as wavelets, wavelet multi-resolution analysis, wavelet packets, wavelets and wavelet packet decomposition/synthesis algorithms, etc. Establish new thinking to understand typical cutting-edge issues in contemporary science based on wavelet thought, and cultivate and improve learners' innovative research capabilities in using wavelet methods and theories to solve scientific and technological problems.
The main content of the course "Wavelets and Science" includes a brief history of wavelets, basic properties of wavelets and wavelet transforms, wavelet multi-resolution analysis methods, wavelet construction and examples, wavelet packet theory, wavelets and time-frequency localization of wavelet packets, wavelet and wavelet packet decomposition/synthesis algorithm, image wavelet transform and wavelet packet transform, image wavelet and wavelet packet pyramid algorithm, wavelet application topics: wavelet packets and uncertainty principle, wavelet and signal filtering and image filtering, wavelet application topics : Wavelet and image compression, etc.

• Chapter 1：Wavelet Manifesto (5 minutes and 15 seconds)

• Chapter 2：The bud of wavelet and the origin of wavelet (10 minutes and 33 seconds)

• Chapter 3：The first example of wavelet sprouting (10 minutes and 57 seconds)

• Chapter 4：Wavelet sprout wavelet prototype (11 minutes and 10 seconds)

• Chapter 5：Obscure Charm Binary Block Theory (8 minutes and 47 seconds)

• Chapter 6：Lusin Theory of Obscure Charm (8 minutes and 25 seconds)

• Chapter 7：Obscure Charm Atomic Decomposition with Morlet Wavelets (15 minutes and 53 seconds)

• Chapter 8：Obscure Charm Three Types of Wavelet Concepts (10 minutes and 39 seconds)

• Chapter 9：Phoenix Nirvana Wavelet Fusion (10 minutes and 38 seconds)

• Chapter 10：Phoenix Nirvana Scientific Symphony (7 minutes and 39 seconds)

• Chapter 11：Phoenix Nirvana Wavelet Temple (6 minutes and 53 seconds)

• Chapter 12：Points and linear spaces (10 minutes and 26 seconds)

• Chapter 13：infinite dimensional linear space (11 minutes and 56 seconds)

• Chapter 14：Vectors and coordinates (12 minutes and 47 seconds)

• Chapter 15：Linear transformation bases and matrices (12 minutes and 1 seconds)

• Chapter 16：linear transformation similarity matrix (7 minutes and 40 seconds)

• Chapter 17：Linear transformation diagonalization and fast algorithm (15 minutes and 36 seconds)

• Chapter 18：Fourier series (12 minutes and 12 seconds)

• Chapter 19：Fourier transform forward and inverse transform (10 minutes and 7 seconds)

• Chapter 20：Typical applications of Fourier transform (10 minutes and 6 seconds)

• Chapter 21：Fourier transform diagonal characteristic relation matrix (11 minutes and 13 seconds)

• Chapter 22：Fourier transform diagonal quadratic transform kernel (7 minutes and 39 seconds)

• Chapter 23：Fourier transform diagonalization diagonalization matrix (10 minutes and 28 seconds)

• Chapter 24：Continuous Wavelet Fluctuation and Decay (10 minutes and 45 seconds)

• Chapter 25：Continuous Wavelet Scaling and Translation True/False Questions (14 minutes and 8 seconds)

• Chapter 26：Wavelet transform and calculation examples (17 minutes and 19 seconds)

• Chapter 27：Unity property of wavelet transform (21 minutes and 17 seconds)

• Chapter 28：Inverse wavelet transform Inverse of unitary transform (12 minutes and 9 seconds)

• Chapter 29：Logic proof of wavelet inverse transform (8 minutes and 33 seconds)

• Chapter 30：Absorption unitary judgment questions of absorption wavelet and wavelet transform (10 minutes and 51 seconds)

• Chapter 31：Absorption wavelet and wavelet transform semi-axis absorption (7 minutes and 59 seconds)

• Chapter 32：Stability conditions of binary wavelet transform (11 minutes and 9 seconds)

• Chapter 33：Binary Wavelet Transform Existence True/False Questions True/False Questions (7 minutes and 19 seconds)

• Chapter 34：Binary wavelet transform dual wavelet (8 minutes and 30 seconds)

• Chapter 35：Dual wavelet and binary wavelet inverse transform judgment questions (14 minutes and 22 seconds)

• Chapter 36：Binary wavelet inverse transform inverse transform formula calculation (11 minutes and 50 seconds)

• Chapter 37：Binary wavelet inverse transform discretization trap (8 minutes and 34 seconds)

• Chapter 38：Orthogonal wavelets and orthogonal series canonical orthogonal wavelet bases (12 minutes and 21 seconds)

• Chapter 39：Orthogonal wavelet and orthogonal series telescopic translation discretization (15 minutes and 2 seconds)

• Chapter 40：Magic wavelet continuous discrete consistency (15 minutes and 14 seconds)

• Chapter 41：Magical orthogonal wavelet mathematical microscope (15 minutes and 12 seconds)

• Chapter 42：Wavelet subspace unitary transform (13 minutes and 10 seconds)

• Chapter 43：Wavelet subspace stretching orthogonality (10 minutes and 29 seconds)

• Chapter 44：Wavelet resolution Definition of resolution (8 minutes and 43 seconds)

• Chapter 45：Wavelet resolutionWavelet multi-resolution (8 minutes and 32 seconds)

• Chapter 46：Scale subspace wavelet components (9 minutes and 23 seconds)

• Chapter 47：Scale subspace multi-resolution approximation (11 minutes and 56 seconds)

• Chapter 48：Scale subspace nesting relationship (9 minutes and 52 seconds)

• Chapter 49：scale subspace monotonicity (12 minutes and 55 seconds)

• Chapter 50：Scale subspace density approximation and density (8 minutes and 46 seconds)

• Chapter 51：Proof of density of scale subspace density (9 minutes and 54 seconds)

• Chapter 52：scale subspace uniqueness (15 minutes and 28 seconds)

• Chapter 53：Scale subspace scalability scaling relationship (13 minutes and 37 seconds)

• Chapter 54：Scale subspace scalability proof (4 minutes and 22 seconds)

• Chapter 55：Scale resolution wavelet and scale subspace (12 minutes and 18 seconds)

• Chapter 56：scale resolution scaling function (12 minutes and 35 seconds)

• Chapter 57：resolution analysis (10 minutes and 34 seconds)

• Chapter 58：Multi-resolution analysis and scaling equation scale functions (8 minutes and 25 seconds)

• Chapter 59：Multi-resolution analysis and scale coefficients of scale equations (8 minutes and 38 seconds)

• Chapter 60：Multi-resolution analysis and low-pass filter frequency domain scaling equation (14 minutes and 27 seconds)

• Chapter 61：Multi-resolution analysis and low-pass filter frequency domain canonical orthogonal basis (9 minutes and 36 seconds)

• Chapter 62：Multi-resolution analysis and low-pass frequency domain identities for low-pass filters (13 minutes and 19 seconds)

• Chapter 63：Multi-resolution analysis and wavelet subspace scaling orthogonality (14 minutes and 21 seconds)

• Chapter 64：Multi-resolution analysis and wavelet subspace hybrid orthogonal decomposition (3 minutes and 58 seconds)

• Chapter 65：Wavelet space decomposition of scale space with complete orthogonal decomposition (14 minutes and 1 seconds)

• Chapter 66：Orthogonal direct sum decomposition of function space and mixed orthogonal decomposition (13 minutes and 30 seconds)

• Chapter 67：Orthogonal direct sum decomposition of function space and complete wavelet subspace decomposition (6 minutes and 30 seconds)

• Chapter 68：Wavelet functions and wavelet equations, orthogonal wavelet conditions (12 minutes and 9 seconds)

• Chapter 69：Translational closure of wavelet functions and wavelet equations (8 minutes and 57 seconds)

• Chapter 70：Simplified and general formulas of wavelet functions and wavelet equations (10 minutes and 39 seconds)

• Chapter 71：Wavelet functions and bandpass filter frequency domain identities (15 minutes and 33 seconds)

• Chapter 72：Bandpass filter impulse response identity sequence space identity (8 minutes and 43 seconds)

• Chapter 73：Band Pass Filter Impulse Response Orthogonality Dual Displacement Orthogonality (9 minutes and 30 seconds)

• Chapter 74：Band Pass Filter Impulse Response Orthogonality Sequence Norm Orthogonality (13 minutes and 6 seconds)

• Chapter 75：Orthogonality of wavelet function and scale function in time domain (11 minutes and 44 seconds)

• Chapter 76：Orthogonality of wavelet function and scale function sequence (8 minutes and 12 seconds)

• Chapter 77：Band pass filter and low pass filter orthogonal conjugation (15 minutes and 2 seconds)

• Chapter 78：Band pass filter and low pass filter wavelet construction matrix (5 minutes and 59 seconds)

• Chapter 79：Characterization of unitary matrix of necessary and sufficient conditions for orthogonal wavelet (11 minutes and 57 seconds)

• Chapter 80：Four-step sufficiency proof for orthogonal wavelet sufficient conditions (9 minutes and 28 seconds)

• Chapter 81：Preliminary knowledge of sufficient conditions for orthogonal wavelets (13 minutes and 45 seconds)

• Chapter 82：Proof of sufficient conditions for orthogonal wavelets I (11 minutes and 39 seconds)

• Chapter 83：Proof of sufficient conditions for orthogonal wavelets II Mixed translational gauge orthogonal system (7 minutes and 10 seconds)

• Chapter 84：Orthogonal Wavelet Sufficient Condition Proof II Mixed Translation Canonical Orthogonal Basis Multiple Choice Questions (14 minutes and 48 seconds)

• Chapter 85：Proof of sufficient conditions for orthogonal wavelets III (12 minutes and 8 seconds)

• Chapter 86：Equivalent form of necessary and sufficient conditions for orthogonal wavelet (14 minutes and 51 seconds)

• Chapter 87：Orthogonal conjugate bandpass filter orthogonal conjugate relationship (9 minutes and 28 seconds)

• Chapter 88：The relationship between the construction of orthogonal wavelets in time domain and frequency domain (12 minutes and 10 seconds)

• Chapter 89：Shannon scale function scale space (14 minutes and 43 seconds)

• Chapter 90：Shannon scale function interpolation function (14 minutes and 13 seconds)

• Chapter 91：Shannon multi-resolution analysis (16 minutes and 41 seconds)

• Chapter 92：Shannon wavelet space low-pass subspace (10 minutes and 3 seconds)

• Chapter 93：Shannon wavelet space bandpass subspace (11 minutes and 47 seconds)

• Chapter 94：Shannon wavelet function (13 minutes and 55 seconds)

• Chapter 95：Shannon wavelet spatial decomposition (13 minutes and 25 seconds)

• Chapter 96：Shannon filter bank low pass filter coefficients (12 minutes and 58 seconds)

• Chapter 97：Shannon filter bank low pass filter (12 minutes and 37 seconds)

• Chapter 98：Shannon wavelet diversity (10 minutes and 47 seconds)

• Chapter 99：Daubechies fundamental theorem of multi-resolution analysis (9 minutes and 22 seconds)

• Chapter 100：Daubechies multi-resolution analysis of tight support conditions (8 minutes and 17 seconds)

• Chapter 101：Daubechies multi-resolution analysis low-pass filter structure (9 minutes and 16 seconds)

• Chapter 102：Requirements for the construction of positive polynomials with canonical real coefficients (11 minutes and 23 seconds)

• Chapter 103：Standard construction of positive polynomials with canonical real coefficients (13 minutes and 41 seconds)

• Chapter 104：Filter and Daubechies wavelet finite term filter (14 minutes and 4 seconds)

• Chapter 105：Filters and Daubechies Wavelets Compactly Supported Wavelets (10 minutes and 25 seconds)

• Chapter 106：Daubechies Wavelet No. 2 (10 minutes and 39 seconds)

• Chapter 107：Daubechies Wavelet No. 3 (11 minutes and 51 seconds)

• Chapter 108：Daubechies Wavelet Diversity Source of Diversity (9 minutes and 3 seconds)

• Chapter 109：Daubechies wavelet diversity typical diversity (11 minutes and 14 seconds)

• Chapter 110：Daubechies wavelet diversity diversity general formula (6 minutes and 48 seconds)

• Chapter 111：Daubechies wavelet diversity diversity example (14 minutes and 16 seconds)

• Chapter 112：Time-frequency analysis and uncertainty principle double window function (7 minutes and 22 seconds)

• Chapter 113：Time-frequency analysis and uncertainty principle time-frequency window (14 minutes and 35 seconds)

• Chapter 114：Time-frequency analysis and uncertainty principleUncertainty principle (4 minutes and 51 seconds)

• Chapter 115：Time-frequency analysis and uncertainty principle Uncertainty principle deduction (12 minutes and 20 seconds)

• Chapter 116：Wavelet and time-frequency analysis wavelet time-frequency window (10 minutes and 33 seconds)

• Chapter 117：Wavelet and time-frequency analysis Wavelet adaptive time-frequency characteristics (12 minutes and 59 seconds)

• Chapter 118：Binary wavelet and time-frequency analysis Binary wavelet time-frequency window (12 minutes and 23 seconds)

• Chapter 119：Binary wavelet and time-frequency analysis band binary segmentation (11 minutes and 37 seconds)

• Chapter 120：Orthogonal wavelet and time-frequency analysis Orthogonal wavelet frequency band (11 minutes and 31 seconds)

• Chapter 121：Orthogonal wavelets and time-frequency analysis frequency bands and wavelet subspaces (8 minutes and 14 seconds)

• Chapter 122：Orthogonal wavelet and time-frequency analysis frequency band segmentation and spatial segmentation (12 minutes and 22 seconds)

• Chapter 123：Orthogonal wavelet and time-frequency analysis wavelet packet idea (8 minutes and 0 seconds)

• Chapter 124：Preliminary knowledge of MALLAT algorithm multi-resolution analysis (11 minutes and 14 seconds)

• Chapter 125：MALLAT algorithm wavelet decomposition and synthesis algorithm decomposition algorithm (10 minutes and 1 seconds)

• Chapter 126：MALLAT algorithm wavelet decomposition and synthesis algorithm synthesis algorithm (7 minutes and 40 seconds)

• Chapter 127：Transition relationship of geometric significance basis of MALLAT algorithm wavelet decomposition algorithm (12 minutes and 21 seconds)

• Chapter 128：MALLAT Algorithm Wavelet Decomposition Algorithm Coordinate Transformation of Geometric Meaning Decomposition (9 minutes and 28 seconds)

• Chapter 129：MALLAT algorithm wavelet synthesis algorithm geometric significance reconstruction equation (11 minutes and 26 seconds)

• Chapter 130：MALLAT algorithm wavelet synthesis algorithm geometric significance reconstruction transitional unitarity (12 minutes and 9 seconds)

• Chapter 131：MALLAT algorithm wavelet synthesis algorithm geometric meaning synthetic coordinate transformation (8 minutes and 28 seconds)

• Chapter 132：MALLAT algorithm wavelet algorithm and multi-resolution analysis matrix wavelet algorithm (9 minutes and 5 seconds)

• Chapter 133：MALLAT algorithm, wavelet algorithm, multi-resolution analysis, decomposition, synthesis and dimensionality improvement (9 minutes and 49 seconds)

• Chapter 134：MALLAT algorithm, wavelet algorithm and multi-resolution analysis, decomposition, synthesis and resolution improvement (7 minutes and 14 seconds)

• Chapter 135：Chain decomposition based on cascade algorithm chain wavelet decomposition algorithm (9 minutes and 4 seconds)

• Chapter 136：Cascade algorithm chain wavelet decomposition algorithm chain decomposition transition relationship (10 minutes and 16 seconds)

• Chapter 137：Cascade algorithm chain wavelet decomposition algorithm chain decomposition coordinate relationship (11 minutes and 8 seconds)

• Chapter 138：Cascade algorithm chain wavelet decomposition algorithm chain decomposition and dimensionality reduction or resolution reduction (9 minutes and 0 seconds)

• Chapter 139：Cascade Algorithm Chain Wavelet Decomposition Geometric Meaning Space and Base Decomposition (14 minutes and 55 seconds)

• Chapter 140：Cascade algorithm chain wavelet decomposition Geometric meaning coordinate decomposition and dimensionality reduction or resolution reduction (9 minutes and 49 seconds)

• Chapter 141：Cascade algorithm chain wavelet decomposition geometric significance function decomposition relationship (8 minutes and 51 seconds)

• Chapter 142：Cascade algorithm chain wavelet synthesis algorithm (13 minutes and 37 seconds)

• Chapter 143：Cascade algorithm chain wavelet synthesis geometric meaning coordinate synthesis relationship (14 minutes and 2 seconds)

• Chapter 144：Cascading Algorithm Chain Wavelet Synthesis Geometric Meaning Chain Synthesis and Dimension Upgrading (13 minutes and 33 seconds)

• Chapter 145：Cascading Algorithm Chain Complete Wavelet Algorithm Theory Transition Matrix of Complete Algorithm (15 minutes and 11 seconds)

• Chapter 146：Cascade algorithm chain complete wavelet algorithm theory matrix coordinate complete algorithm (15 minutes and 4 seconds)

• Chapter 147：Cascade Algorithm Chained Complete Wavelet Algorithm Annotation Graphical Space and Base Algorithm (12 minutes and 23 seconds)

• Chapter 148：Cascade Algorithm Chain Complete Wavelet Algorithm for Annotating Graphical Functions and Coordinates (13 minutes and 36 seconds)

• Chapter 149：Cascade algorithm chain complete wavelet algorithm annotation algorithm ascending and descending dimension relationship (8 minutes and 38 seconds)

• Chapter 150：Cascade Algorithm Chain Complete Wavelet Algorithm Annotation Methodology of Wavelet Algorithm (9 minutes and 37 seconds)

• Chapter 151：Transition matrix for decomposition and synthesis of cascade algorithm sequence spatial chain wavelet algorithm (7 minutes and 57 seconds)

• Chapter 152：Decomposition and synthesis of basis and vector of cascade algorithm sequence space chain wavelet algorithm (10 minutes and 44 seconds)

• Chapter 153：Finite sequence algorithm Finite dimensional space cascade wavelet algorithm Finite dimensional transition matrix (14 minutes and 29 seconds)

• Chapter 154：Finite sequence algorithm Finite dimensional space cascade wavelet algorithm Vector decomposition synthesis relationship (13 minutes and 5 seconds)

• Chapter 155：Finite sequence algorithm, finite dimensional space chain wavelet algorithm, transition relationship and graphical algorithm (10 minutes and 55 seconds)

• Chapter 156：Finite sequence algorithm Finite dimensional space chain wavelet algorithm Vector space algorithm (14 minutes and 59 seconds)

• Chapter 157：Wavelet packet theory multi-resolution analysis and wavelet packet joint decomposer (14 minutes and 57 seconds)

• Chapter 158：Multi-resolution analysis of wavelet packet theory and wavelet packet decomposition theorem (12 minutes and 6 seconds)

• Chapter 159：Wavelet Packet Theory Wavelet Packet and Orthogonality (11 minutes and 38 seconds)

• Chapter 160：Wavelet Packet Theory Wavelet Packet and Subspace Decomposition Subspace Wave Packet Decomposition (14 minutes and 42 seconds)

• Chapter 161：Wavelet packet theory, wavelet packet and subspace decomposition, decomposition of canonical orthogonal basis (14 minutes and 15 seconds)

• Chapter 162：Wavelet packet theory subspace complete decomposition of wavelet packet scale space complete decomposition (11 minutes and 25 seconds)

• Chapter 163：Wavelet packet theory subspace wavelet packet complete decomposition space and complete decomposition of basis (9 minutes and 37 seconds)

• Chapter 164：Wavelet packet theory, wavelet packet decomposition and synthesis algorithm, function decomposition and Pythagorean theorem (9 minutes and 20 seconds)

• Chapter 165：Wavelet packet theory, wavelet packet decomposition and synthesis algorithm, coordinate decomposition and synthesis (12 minutes and 48 seconds)

• Chapter 166：Wavelet packet theory space and basis of wavelet packet complete algorithm complete transition matrix (10 minutes and 22 seconds)

• Chapter 167：The transition relationship between the wavelet packet theory space and the basis of the wavelet packet complete algorithm (14 minutes and 56 seconds)

• Chapter 168：Wavelet packet theory function and coordinates of the wavelet packet complete algorithm space complete decomposition (11 minutes and 11 seconds)

• Chapter 169：Wavelet packet complete algorithm for wavelet packet theory functions and coordinates to completely decompose the transition matrix (11 minutes and 36 seconds)

• Chapter 170：Wavelet packet theory functions and coordinates, wavelet packet complete algorithm function decomposition and the Pythagorean theorem (11 minutes and 50 seconds)

• Chapter 171：Wavelet packet theory function and complete algorithm of wavelet packet for coordinates coordinate transformation and Pythagorean theorem (13 minutes and 43 seconds)

• Chapter 172：Wavelet packet theory, finite dimensional space wavelet packet algorithm, orthogonal periodization (12 minutes and 7 seconds)

• Chapter 173：Wavelet packet theory, finite dimensional space wavelet packet algorithm decomposition and dimensionality reduction (9 minutes and 42 seconds)

• Chapter 174：Wavelet packet theory, finite dimensional space wavelet packet algorithm synthesis algorithm and Pythagorean theorem (7 minutes and 16 seconds)

• Chapter 175：Wavelet packet theory Matrix mode for decomposition and synthesis of wavelet packet algorithm in finite dimensional space (11 minutes and 49 seconds)

• Chapter 176：Two-dimensional wavelet two-dimensional multi-resolution analysis and wavelet tensor product idea (14 minutes and 43 seconds)

• Chapter 177：Two-dimensional wavelet, two-dimensional multi-resolution analysis and wavelet two-dimensional wavelet space (11 minutes and 25 seconds)

• Chapter 178：Two-dimensional wavelet, two-dimensional multi-resolution analysis and wavelet, two-dimensional orthogonal wavelet (10 minutes and 16 seconds)

• Chapter 179：Transition relationship between two-dimensional wavelet two-dimensional multi-resolution analysis and wavelet decomposition (9 minutes and 29 seconds)

• Chapter 180：Two-dimensional wavelet Preliminary knowledge of decomposition and synthesis algorithm of two-dimensional wavelet (14 minutes and 40 seconds)

• Chapter 181：Two-dimensional wavelet Decomposition and synthesis algorithm of two-dimensional wavelet Scale space orthogonal decomposition (11 minutes and 49 seconds)

• Chapter 182：Two-dimensional wavelet Decomposition and synthesis algorithm of two-dimensional wavelet Wavelet space expansion and contraction (9 minutes and 7 seconds)

• Chapter 183：Two-dimensional wavelet Decomposition and synthesis of two-dimensional wavelet Algorithm base decomposition and reconstruction (11 minutes and 31 seconds)

• Chapter 184：Two-dimensional wavelet Decomposition and synthesis algorithm of two-dimensional wavelet Matrix format of basis decomposition and synthesis (9 minutes and 16 seconds)

• Chapter 185：Two-dimensional wavelet decomposition and synthesis algorithm of two-dimensional wavelet coordinate decomposition synthesis and matrix format (9 minutes and 35 seconds)

• Chapter 186：Two-dimensional wavelet Two-dimensional wavelet pyramid algorithm Scale space tower decomposition (12 minutes and 22 seconds)

• Chapter 187：Tower decomposition of two-dimensional wavelet and two-dimensional wavelet pyramid algorithm bases (8 minutes and 6 seconds)

• Chapter 188：Two-dimensional wavelet, two-dimensional wavelet pyramid algorithm, multi-level decomposition of scale space and basis (12 minutes and 9 seconds)

• Chapter 189：Two-dimensional wavelet Two-dimensional wavelet pyramid algorithm Orthogonal decomposition of images (8 minutes and 58 seconds)

• Chapter 190：Matrix format of coefficient decomposition and synthesis of two-dimensional wavelet and two-dimensional wavelet pyramid algorithm (11 minutes and 57 seconds)

• Chapter 191：Two-dimensional wavelet, two-dimensional wavelet pyramid algorithm, coefficient decomposition, multi-level joint matrix format (9 minutes and 20 seconds)

• Chapter 192：Two-dimensional wavelet, two-dimensional wavelet pyramid algorithm coefficient synthesis, multi-level joint matrix format (10 minutes and 19 seconds)

• Chapter 193：Two-dimensional wavelet two-dimensional wavelet pyramid algorithm coefficients with the same resolution synthesis matrix format (10 minutes and 19 seconds)

• Chapter 194：Two-dimensional wavelet packet Two-dimensional wavelet packet theory Two-dimensional orthogonal wavelet basis (11 minutes and 45 seconds)

• Chapter 195：Two-dimensional wavelet packet Two-dimensional wavelet packet theory Orthogonal decomposition of two-dimensional wavelet packet space (10 minutes and 2 seconds)

• Chapter 196：Two-dimensional wavelet packet Two-dimensional wavelet packet theory Two-dimensional wavelet packet canonical orthogonal basis (7 minutes and 27 seconds)

• Chapter 197：Two-dimensional wavelet packet Decomposition and synthesis algorithm of two-dimensional wavelet packet Two-dimensional scale and wavelet equation (8 minutes and 44 seconds)

• Chapter 198：Two-dimensional wavelet packet decomposition and synthesis algorithm of two-dimensional wavelet packet spatial decomposition of two-dimensional wavelet packet (8 minutes and 20 seconds)

• Chapter 199：Two-dimensional wavelet packet Decomposition and synthesis algorithm of two-dimensional wavelet packet Wavelet packet decomposition and synthesis of image (14 minutes and 37 seconds)

• Chapter 200：Two-dimensional wavelet packet Decomposition and synthesis algorithm of two-dimensional wavelet packet Two-dimensional wavelet packet decomposition and synthesis matrix format (11 minutes and 17 seconds)

• Chapter 201：Two-dimensional wavelet packet, two-dimensional wavelet packet pyramid algorithm, tower decomposition and synthesis of images and coefficients (9 minutes and 41 seconds)

• Chapter 202：Two-dimensional wavelet packet, two-dimensional wavelet packet pyramid algorithm, image multi-level tower decomposition and synthesis joint format (13 minutes and 33 seconds)

• Chapter 203：Digital image algorithm Two-dimensional wavelet decomposition and synthesis algorithm Digital image decomposition and synthesis matrix format (10 minutes and 12 seconds)

• Chapter 204：Digital image algorithm Two-dimensional wavelet decomposition and synthesis algorithm Digital image multi-level decomposition and synthesis matrix format (6 minutes and 1 seconds)

• Chapter 205：Digital image algorithm Two-dimensional wavelet packet decomposition and synthesis algorithm Digital image complete wavelet packet decomposition joint format (13 minutes and 53 seconds)

• Chapter 206：Digital image algorithm Two-dimensional wavelet packet decomposition and synthesis algorithm Digital image complete wavelet packet synthesis joint format (13 minutes and 14 seconds)

• Chapter 207：The scientific significance of wavelets and wavelet packets and the numerical significance of wavelet transforms (11 minutes and 4 seconds)

• Chapter 208：The scientific significance of wavelets and wavelet packets and the image significance of wavelet transform (10 minutes and 5 seconds)

• Chapter 209：The scientific significance of wavelets and wavelet packets and the significance of orthogonal wavelet spectroscopy (5 minutes and 49 seconds)

• Chapter 210：The scientific significance of wavelets and wavelet packets and the significance of orthogonal wavelet transform coefficient matrices (6 minutes and 18 seconds)

• Chapter 211：The scientific significance of wavelets and wavelet packets The significance of multi-resolution analysis (13 minutes and 21 seconds)

• Chapter 212：The scientific significance of wavelets and wavelet packets The significance of wavelet cascade algorithm (6 minutes and 28 seconds)

• Chapter 213：The scientific significance of wavelets and wavelet packets The scientific significance of wavelet packet fields (10 minutes and 44 seconds)

• Chapter 214：The scientific significance of wavelets and wavelet packets The significance of two-dimensional wavelet packets (8 minutes and 12 seconds)

• Chapter 215：The scientific significance of wavelets and wavelet packets The significance of light fields and image wavelet packets (8 minutes and 3 seconds)

• Chapter 216：The scientific significance of wavelets and wavelet packets The mathematical microscopic significance of wavelets and wavelet packets (6 minutes and 55 seconds)

• Chapter 217：Wavelet packets and the uncertainty principle Wavelet packets adapt to the uncertainty principle (6 minutes and 11 seconds)

• Chapter 218：Wavelet packets and the uncertainty principle Wavelet packets break through the uncertainty principle (10 minutes and 43 seconds)

• Chapter 219：Wavelet packets and the universality of the uncertainty principle in the wavelet packet domain (6 minutes and 54 seconds)

• Chapter 220：Wavelet and wavelet cascade expression of signal (7 minutes and 30 seconds)

• Chapter 221：Wavelets and wavelet packets of signals are fully expressed (8 minutes and 39 seconds)

• Chapter 222：Wavelet and Signal Signal Wavelet Analysis Demonstration (5 minutes and 24 seconds)

• Chapter 223：Wavelet and Signal Signal Wavelet Packet Processing Demonstration (7 minutes and 27 seconds)

• Chapter 224：Wavelet and image light field and wavelet packet expression of image (14 minutes and 36 seconds)

• Chapter 225：Wavelet and Image Image Wavelet Packet Processing Demonstration (10 minutes and 52 seconds)

• Chapter 226：Wavelet and fast calculation of circular convolution (7 minutes and 23 seconds)

• Chapter 227：Wavelet and fast calculation of finite Fourier transform and convolution diagonalization (11 minutes and 23 seconds)

• Chapter 228：Wavelet and fast calculation of convolution operator fast algorithm (6 minutes and 9 seconds)

• Chapter 229：Wavelet and fast calculation operator of wavelet and wavelet packet fast algorithm (7 minutes and 37 seconds)

• Chapter 230：Wavelet packets and light field images and wavelet packet theory of light fields (8 minutes and 44 seconds)

• Chapter 231：Wavelet packets and light fields Complete wavelet packet theory of light fields (7 minutes and 7 seconds)