This paper presents a novel multi-frame joint learning approach for image super resolution via sparse representation. Based on the assumption that several low-resolution patches degraded from a same high-resolution patch under subpixel translation can preserve similar structures, we can use those similar low-resolution patches together to recover the sparse coefficients for the corresponding high-resolution patch, and the differences between them can help to supply more information. So, unlike the learning-based super resolution algorithm from single image which uses one patch in the learning process, we take into consideration some other well matched patches in 3D domain. Computer simulations demonstrate that, comparing with those single frame learning algorithms, our method will not only restore more details but also can effectively overcome the over learning and is more robust to noise.
In this paper, the one-dimensional principal component lter banks (PCFB's) derived in 17] are generalized to higher dimensions. As presented in 17], PCFB's minimize the mean-squared error (MSE) when only Q out of P subbands are retained. Previously, 2D PCFB's were proposed in 16]. The work in 16] was limited to 2D signals and separable resampling operators. The formulation presented here is general in that it can easily accommodate signals of arbitrary (yet nite) dimension and non-separable sampling. A major result presented in this paper is that in addition to minimizing MSE when reconstructing from Q out of P subbands, the PCFB's result in maximizing theoretical coding gain (TCG) y This work was supported in part by the National Science Foundation under grants NCR-9303868, MIP-9116683, USE-9250721, and CDA-9121675. Dr. Bamberger is the contact author. z EDICS Category: SP 2.4.2. Permission to publish this abstract separately is granted. Actually, the PCFB's maximize the arithmetic mean to geometric mean ratio (AM/GM ratio) of subband LIST OF TABLES 1. MSE and TCG (dB) Comparison between PCFB and Trad. Separable FB LIST OF FIGURES 1. Fundamental Coset Vectors for Resampling Matrices with J(M) = 4 2. A Typical P-band Paraunitary Filter Bank 3. A Polyphase Representation of a P-band Paraunitary Filter Bank 4. The Power Spectral Density of a Stationary Input (top) and the Corresponding PCFB for M= 4 3;0 1] (bottom) 5. The First Subband Analysis Filter and Reconstructed Image Retaining only One Subband for M= 4 0;0 1] Using PCFB (top) and Trad. Parallelogram FB Implemented via a 32-tap 1D Filter (bottom) 6. The First Subband Analysis Filter and Reconstructed Image Retaining only One Subband for M= 4 1;0 1] Using PCFB (top) and Trad. Parallelogram FB Implemented via a 32-tap 1D Filter (bottom) 7. The First Subband Analysis Filter and Reconstructed Image Retaining only One Subband for M= 4 2;0 1] Using PCFB (top) and Trad. Parallelogram FB Implemented via a 32-tap 1D Filter (bottom) 8. The First Subband Analysis Filter and Reconstructed Image Retaining only One Subband for M= 4 3;0 1] Using PCFB (top) and Trad. Parallelogram FB Implemented via a 32-tap 1D Filter (bottom) 9. The First Subband Analysis Filter and Reconstructed Image Retaining only One Subband for M= 2 0;0 2] Using PCFB (top) and Trad. Parallelogram FB Implemented via a 32-tap 1D Filter (bottom) 10. The First Subband Analysis Filter and Reconstructed Image Retaining only One Subband for M= 2 1;0 2] Using PCFB (top) and Trad. Parallelogram FB Implemented via a 32-tap 1D Filter (bottom) 11. The First Subband Analysis Filter and Reconstructed Image Retaining only One Subband for M= 1 0;0 4] Using PCFB (top) and Trad. Parallelogram FB Implemented via a 32-tap 1D Filter (bottom) v 12. The Transform E ciency for the Cameraman Image Using PCFB's and Traditional FB's 13. TCG Comparison for the Cameraman Image Using PCFB's and Traditional FB's
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