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Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering of the frame expansion coefficients. Compared to ordinary permutation source coding, FPQ produces a greater number of… (More)
—Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the simplicity of encoding while increasing the number of rate–distortion operating points, improving the convex hull of operating… (More)
Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure. In this paper, we provide an extension that preserves the computational simplicity but yields improved operational rate-distortion performance. The new class of vector quantizers has a codebook comprising several permutation codes as subcodes.… (More)
A MUSIC-like algorithm is proposed to solve a specific matrix factorization problem.
In this note we attempt to provide another approach to the matrix factorization problem arisen in image relighting, which is more computationally efficient compared to the original approach in .
—As a generalization of the subspace fitting, the union of subspaces fitting problem consists in finding an union of subspaces in some given family that best fits to the finite data. This report provides a detailed review of the main reference  about the existence of such optimal solution. Proofs for a series of unproved statements in the reference are… (More)
The key bound which was used unnaturally in Gallager's paper is justified through some basic inequalities. The random coding exponent function defined by Gallager can be derived from Csiszar's approach.
—Quantized frame expansions are overcomplete representations of signals approximated by some quantizer. This scheme proved to be a very useful tool to combat quantization noise and erasures. Normally, a scalar quantizer is used in the quantization phase. In this paper we investigate the use of permutation codes, a beautiful source coding technique, as a… (More)
The algorithm proposed in  turns out to be costly in computing the extended SVD of a big matrix. In this note, the algorithm is modified slightly to get rid of the extended SVD. The novel algorithm is only involved with the regular SVD.
Permutation source codes are a class of structured vector quantizers with a computa-tionally-simple encoding procedure. In this thesis, we provide two extensions that preserve the computational simplicity but yield improved operational rate–distortion performance. In the first approach, the new class of vector quantizers has a codebook comprising several… (More)