8. An image processing apparatus configured to perform image processing to convert an image, the image processing apparatus comprising: a coefficient calculator configured to perform, on each of multiple first dictionaries produced by dictionary learning, a process to approximate a first image by linear combination of elements of the first dictionary so as to produce a linear combination coefficient and thereby acquiring multiple linear combination coefficients; a coefficient selector configured to calculate, for each of the multiple linear combination coefficients, a ratio between a largest coefficient element and a second-largest coefficient element among respective coefficient elements of the respective linear combination coefficients, the largest coefficient element having an absolute value that is largest among the respective coefficient elements and the second-largest coefficient element having an absolute value that is second-largest among the respective coefficient elements, thereby obtaining respective ratios of the multiple linear combination coefficients, and to select a specific linear combination coefficient, among the multiple linear combination coefficients, having the ratio that is largest among the respective ratios of the multiple linear combination coefficients; a dictionary selector configured to select, from multiple second dictionaries corresponding to the first dictionaries, a specific dictionary corresponding to the first dictionary for which the specific linear combination coefficient is selected; and an image producer configured to convert the first image into a second image by using linear combination of the specific linear combination coefficient and elements of the specific dictionary.
8. An image processing apparatus configured to perform image processing to convert an image, the image processing apparatus comprising: a coefficient calculator configured to perform, on each of multiple first dictionaries produced by dictionary learning, a process to approximate a first image by linear combination of elements of the first dictionary so as to produce a linear combination coefficient and thereby acquiring multiple linear combination coefficients; a coefficient selector configured to calculate, for each of the multiple linear combination coefficients, a ratio between a largest coefficient element and a second-largest coefficient element among respective coefficient elements of the respective linear combination coefficients, the largest coefficient element having an absolute value that is largest among the respective coefficient elements and the second-largest coefficient element having an absolute value that is second-largest among the respective coefficient elements, thereby obtaining respective ratios of the multiple linear combination coefficients, and to select a specific linear combination coefficient, among the multiple linear combination coefficients, having the ratio that is largest among the respective ratios of the multiple linear combination coefficients; a dictionary selector configured to select, from multiple second dictionaries corresponding to the first dictionaries, a specific dictionary corresponding to the first dictionary for which the specific linear combination coefficient is selected; and an image producer configured to convert the first image into a second image by using linear combination of the specific linear combination coefficient and elements of the specific dictionary. 9. The image processing apparatus according to claim 8 , wherein: the second image is an image showing a result of classifying multiple types of object images contained in the first image, and further comprising a provider configured to provide the multiple first and second dictionaries produced by the dictionary learning that uses a first training image relevant to the first image and multiple vector data as a second training image showing the types of the respective object images; wherein: the coefficient calculator is configured to perform, on each of the multiple first dictionaries, a process to approximate a partial image extracted from the first image by the linear combination of the elements of the first dictionary so as to produce a linear combination coefficient and thereby acquiring the multiple linear combination coefficients, and then selecting the specific linear combination coefficient from the multiple linear combination coefficients; and the image producer is configured (a) to producing a classification vector by using the linear combination of the specific linear combination coefficient and the elements of the specific dictionary and determining the type of the object image in the partial image by using the classification vector, (b) to perform, on each of the partial images plurally extracted from the entire first image, the selection of the specific linear combination coefficient and the determination of the type of the object image using the classification vector and the multiple vector data, and (c) to produce the second image depending on the type of the object image determined in each of the partial images.