An optimal recovery approach to interpolation

Prediction of image detail

“…4) and then decimate by two to obtain In [5] it was shown that the optimal interpolation filter for a prefiltered (with linear filter ) and down-sampled image, in the Golomb-Weinberger sense, is the autocorrelation function of . In our example, we have filtered the down-sampled image with the autocorrelation of the decimation filter (which turns out to be cubic interpolation) to obtain the cubic interpolated image of Fig.…”

Super-resolution using neural networks based on the optimal recovery theory

“…A lot of image reconstruction algorithms based on the optimal recovery theory arise recently [23,[25][26][27][28]. Although quite different from each other, they benefit from the common strengths intrinsic to the optimal recovery representation: the subjective quality of output images is satisfactory [27].…”

“…(e) Partial Differential Equation (PDE) models [23,24] establish inter-pixel correlation from a more abstract point of view, yet they usually yield images with jagged artifacts and are vulnerable to noises. (f) Optimal recovery interpolators [23,[25][26][27], and (g) Neural-network based methods [29][30][31], which are to be detailed in Section 2.…”

“…Such resolution enhancement techniques may be generally referred to as Super Resolution (SR) image reconstruction, which primarily consists of three categories: (a) Multiple-frame SR by extracting a single HR image from a sequence of Low-Resolution (LR) images aligned in sub-pixel accuracy (see [1][2][3] for excellent surveys) (b) Single-frame example-based SR that increases the resolution of a single image with training based on analogous images [4][5][6][7][8][9][10][11][29][30][31] (c) Single-frame SR that does not depend on any other images [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. The latter category of single-frame SR is more commonly referred to as image interpolation or digital zooming.…”

Color LAR Codec: A Color Image Representation and Compression Scheme Based on Local Resolution Adjustment and Self-Extracting Region Representation

“…To achieve edge interpolation (2 × 2 blocks), we have selected a directional interpolation algorithm designed by D. Muresan [25], based on the optimal adaptive recovery of missing values. This technique, developed by Golomb [26], was initially applied by Shenoy and Parks to interpolation [27]. Figure 3 shows post-processing used to smooth uniform areas while preserving sharp edges [28].…”