Least-squares reconstruction of objects with missing high-frequency components

Rushforth, C.K.; Crawford, Andrew; Zhou, Y.

doi:10.1364/josa.72.000204

Cited by 38 publications

(7 citation statements)

References 3 publications

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“…We see a trade-off between detection power and false-alarm rate. Figure 5 shows the detection power 1 − ␤͑x ᠬ ͒ as a function of the relative offset parameter ʈx ᠬ ʈ A / ͑L͒ for ␣ = 0.05 and L / A 2 = 10 and SNR͑0͒ =2, 4,6,8,10. For large offsets the detection power approaches ␣, since then the point source has little effect on the measurements.…”

Section: ͑9͒mentioning

confidence: 99%

“…This is known as superresolution. [3][4][5][6][7][8][9][10][11][12] Indeed, the frequency components of an input image of finite extent that have not been transmitted through the band-limited imaging system may still be recovered by the technique of analytic continuation or other postprocessing methods. However, it is well known that this problem is ill-posed; i.e., small noise present in the data results in large error in the estimation.…”

Section: Introductionmentioning

confidence: 99%

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Broadband resolution analysis for imaging with measurement noise

Fannjiang

Sølna

2007

J. Opt. Soc. Am. A

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Section: ͑9͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Broadband resolution analysis for imaging with measurement noise

Fannjiang

Sølna

2007

J. Opt. Soc. Am. A

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“…From (19) and (20), the'inequality in (21) follows. The recursive implementation analogous to (26), (27), and (28) also can be obtained.…”

Section: Recursive Restoration Of Bilinearly Degraded Images a 1-d Imentioning

confidence: 99%

Approaches toward restoration of bilinearly degraded images

Kim

Bose

1987

IEEE Trans. Acoust., Speech, Signal Process.

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In response to the practical need for restoring images which are degraded by systems which are bilinear, this paper focuses on the development and application of tools required for this purpose. When the blurring phenomenon can be modeled by a shift-variant bilinear system, the data restoration problem can be most conveniently formulated as a special system of linear equations with nonnegative coefficients, whose solution is required to satisfy constraints like nonnegativity in addition to it being factorable with the factors having a certain characterizing property. Recursive techniques for restoration are first developed when the blurring system is either causal or weakly causal. It is shown how these recursive techniques when applied several times and the solutions superposed can, sometimes, be used to restore images degraded by noncausal blurs. Algorithms based on noniterative and iterative schemes are, subsequently, developed to tackle directly the noncausal blurs. Performances of the various algorithms when applied to noisy images are briefly compared.

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“…The effects of the noise contained in the input pattern on the output vector are clearly understood with singular values in the pseudoinverse. 5,6 Since small singular values amplify the noise, we modify the small singular values by replacing them with a specified value. We recognize alphabet characters with a better memory matrix, which is generated by manipulating the singular values.…”

Section: Introductionmentioning

confidence: 99%

Optical character recognition using a memory matrix generated from singular value decomposition

et al. 1998

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A memory matrix provides output vectors that are specified by the corresponding input vectors. If the input vectors represent input characters, the memory matrix performs character recognition. When the input characters contain noise, it is difficult to recognize the characters. To overcome this difficulty, we generate a new memory matrix by using singular value decomposition and manipulating the singular values. The effectiveness of the memory matrix is made clear by recognizing 26 alphabets characters containing noise with an optical recognition system.

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Least-squares reconstruction of objects with missing high-frequency components

Cited by 38 publications

References 3 publications

Broadband resolution analysis for imaging with measurement noise

Broadband resolution analysis for imaging with measurement noise

Approaches toward restoration of bilinearly degraded images

Optical character recognition using a memory matrix generated from singular value decomposition

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