Vector space, norms, distances and inner products. Complete spaces.
Hilbert spaces. Linear operators on Hilbert spaces. Bounded operators.
Inverse operators. Adjoint operators. Projection operators. Bases of a
vector space. Riesz bases. Frames. Tight frames. Mean Square Error
approximation. Properties and families of matrices. Time-Frequency
representation. Heisenberg uncertainty principle. Continuous wavelet
transform. Short-time Fourier transform (STFT). Continuous transform
sampling. Discrete STFT, Discrete wavelet transform. Continuous-time
signal linear expansions using wavelet series. Haar transform. Filterbanks
for discrete time signal representation. Multiresolution decomposition.
Applications: Denoising, In-painting, Coding, ... Elements of Compressive
sensing. (Orthogonal) Matching Pursuit.