Atul Divekar - Academia.edu (original) (raw)
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ABSTRACT We propose a new method of image fusion that utilizes the recently developed theory of c... more ABSTRACT We propose a new method of image fusion that utilizes the recently developed theory of compressive sensing. Compressive sensing indicates that a signal that is sparse in an appropriate set of basis vectors may be recovered almost exactly from a few samples via l1-minimization if the system matrix satisfies some conditions. These conditions are satisfied with high probability for Gaussian-like vectors. Since zero-mean image patches satisfy Gaussian statistics, they are suitable for compressive sensing. We create a dictionary that relates high resolution image patches from a panchromatic image to the corresponding filtered low resolution versions. We first propose two algorithms that directly use this dictionary and its low resolution version to construct the fused image. To reduce the computational cost of l1-minimization, we use principal component analysis to identify the orthogonal "modes" of co-occurrence of the low and high resolution patches. Any pair of co-occurring high and low resolution patches with similar statistical properties to the patches in the dictionary is sparse with respect to the principal component bases. Given a patch from a low resolution multispectral band image, we use l1-minimization to find the sparse representation of the low resolution patch with respect to the sample-domain principal components. Compressive sensing suggests that this is the same sparse representation that a high resolution image would have with respect to the principal components. Hence the sparse representation is used to combine the high resolution principal components to produce the high resolution fused image. This method adds high-resolution detail to a low-resolution multispectral band image keeping the same relationship that exists between the high and low resolution versions of the panchromatic image. This reduces the spectral distortion of the fused images and produces results superior to standard fusion methods such as the Bro- vey transform and principal component analysis.
Image databases, medical records and geographical information systems contain data that is intrin... more Image databases, medical records and geographical information systems contain data that is intrinsically correlated, i.e. elements within a single single record show a high degree of correlation. Content based retrieval is a common technique for querying such databases. The query specifies an image or components that the record is expected to contain or be similar to.We propose a technique for compact storage of such correlated data that is used for content based retrieval . Our method utilizes the machinery of compressive sensing, which allows an under determined system of equations to be approximately solved by l1-minimization if the data is a sparse linear combination of an appropriate set of basis vectors. Such sparsity is seen in these correlated databases. If the sparsity is high or if some distortion is permitted in the retrieved data, the data can be retrieved by a reconstruction operation with a constant storage cost independent of the number of records stored. If exact retrieval is needed, some additional storage is required for each record, much smaller than the size of the original record. We illustrate the performance of this method with a database of remote sensing images.
Compressive Sensing is a recently developed technique that exploits the sparsity of naturally occ... more Compressive Sensing is a recently developed technique that exploits the sparsity of naturally occurring signals and images to solve inverse problems when the number of samples is less than the size of the original signal. We apply this technique to solve underdetermined inverse problems that commonly occur in remote sensing, including superresolution, image fusion and deconvolution. We use l 1 -minimization to develop algorithms that perform as well as or better than conventional methods for these problems. Our algorithms use a library of samples from similar images or a model for the image to be reconstructed to express the image as a sparse linear combination. A set of feature vectors is generated from the library or basis and is used to find the sparsest linear combination that matches the data using l 1 -minimization.
... Atul Divekar, Okan Ersoy, ... 2 Page 6. 1: // Input: M by N matrix Φ, sample vector y = Φc 2:... more ... Atul Divekar, Okan Ersoy, ... 2 Page 6. 1: // Input: M by N matrix Φ, sample vector y = Φc 2: // Output:AK′ − 1 sparse approximation u of c 3: for n = 1 to MaxIter do 4: J ← ∅, R ← {1..N}, r ← y 5: k ← 1 6: while k ≤ Km and ||r|| > 0 do 7: z ← ΦT Rr. 8: For each i ∈ R, assign pi. ...
ABSTRACT We propose a new method of image fusion that utilizes the recently developed theory of c... more ABSTRACT We propose a new method of image fusion that utilizes the recently developed theory of compressive sensing. Compressive sensing indicates that a signal that is sparse in an appropriate set of basis vectors may be recovered almost exactly from a few samples via l1-minimization if the system matrix satisfies some conditions. These conditions are satisfied with high probability for Gaussian-like vectors. Since zero-mean image patches satisfy Gaussian statistics, they are suitable for compressive sensing. We create a dictionary that relates high resolution image patches from a panchromatic image to the corresponding filtered low resolution versions. We first propose two algorithms that directly use this dictionary and its low resolution version to construct the fused image. To reduce the computational cost of l1-minimization, we use principal component analysis to identify the orthogonal "modes" of co-occurrence of the low and high resolution patches. Any pair of co-occurring high and low resolution patches with similar statistical properties to the patches in the dictionary is sparse with respect to the principal component bases. Given a patch from a low resolution multispectral band image, we use l1-minimization to find the sparse representation of the low resolution patch with respect to the sample-domain principal components. Compressive sensing suggests that this is the same sparse representation that a high resolution image would have with respect to the principal components. Hence the sparse representation is used to combine the high resolution principal components to produce the high resolution fused image. This method adds high-resolution detail to a low-resolution multispectral band image keeping the same relationship that exists between the high and low resolution versions of the panchromatic image. This reduces the spectral distortion of the fused images and produces results superior to standard fusion methods such as the Bro- vey transform and principal component analysis.
Image databases, medical records and geographical information systems contain data that is intrin... more Image databases, medical records and geographical information systems contain data that is intrinsically correlated, i.e. elements within a single single record show a high degree of correlation. Content based retrieval is a common technique for querying such databases. The query specifies an image or components that the record is expected to contain or be similar to.We propose a technique for compact storage of such correlated data that is used for content based retrieval . Our method utilizes the machinery of compressive sensing, which allows an under determined system of equations to be approximately solved by l1-minimization if the data is a sparse linear combination of an appropriate set of basis vectors. Such sparsity is seen in these correlated databases. If the sparsity is high or if some distortion is permitted in the retrieved data, the data can be retrieved by a reconstruction operation with a constant storage cost independent of the number of records stored. If exact retrieval is needed, some additional storage is required for each record, much smaller than the size of the original record. We illustrate the performance of this method with a database of remote sensing images.
Compressive Sensing is a recently developed technique that exploits the sparsity of naturally occ... more Compressive Sensing is a recently developed technique that exploits the sparsity of naturally occurring signals and images to solve inverse problems when the number of samples is less than the size of the original signal. We apply this technique to solve underdetermined inverse problems that commonly occur in remote sensing, including superresolution, image fusion and deconvolution. We use l 1 -minimization to develop algorithms that perform as well as or better than conventional methods for these problems. Our algorithms use a library of samples from similar images or a model for the image to be reconstructed to express the image as a sparse linear combination. A set of feature vectors is generated from the library or basis and is used to find the sparsest linear combination that matches the data using l 1 -minimization.
... Atul Divekar, Okan Ersoy, ... 2 Page 6. 1: // Input: M by N matrix Φ, sample vector y = Φc 2:... more ... Atul Divekar, Okan Ersoy, ... 2 Page 6. 1: // Input: M by N matrix Φ, sample vector y = Φc 2: // Output:AK′ − 1 sparse approximation u of c 3: for n = 1 to MaxIter do 4: J ← ∅, R ← {1..N}, r ← y 5: k ← 1 6: while k ≤ Km and ||r|| > 0 do 7: z ← ΦT Rr. 8: For each i ∈ R, assign pi. ...